Point P(x,y) moves with a distance from (0,1) one-half of its distance from line y = 4. What is the equation of the locus?

Q: An ant is walking on the xy-plane is such a way that its distance to the point (2, 4) is always the…

A: Solution: Let the point P(x,y) is the position of Ant and given that the distance from P(x,y) to…

Q: A circle passes through the point (6, 2). If segments of the straight lines x + y = 6 and x + 2y = 4…

A: We can find the radius as below.

Q: The circle whose equation is ((x+3)^2)+((y+4)^2)=17 and the line whose equation is y= 4x+25 are…

A: Given query is to find the the point of tangency.

Q: Find the equation of locus of a point which is at a distance 5 from A (4, -3).

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Q: Point A is located at (-1, -5). The midpoint of line segment AB is point C(2, 3). What are the…

A: Given , Point A is located at (-1,-5).the mid point of line segment AB is point C(2,3).we have to…

Q: The equation of the tangent line to the circle x^2 + y^2 = 36 at the point (5, square root 11) is…

A:

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13=0 in which the tangent line…

A:

Q: A straight connecting street segment is built perpendicular to an existing street with equation y…

A: Given,            y = 27x + 3 and point =-1, -0.2

Q: Find the equation of a line tangent to a circle whose equation is x2 + y2 – 4x - 21 = 0 at point…

A: Given equation of circle x2+y2-4x-21=0

Q: Point (x ,y) distance from Q А (5,5) (2,3) (1,1) V20 В 1 C 6. A 5

A: Given: A(5,5) B(2,3) C(1,1) AQ=20 BQ=1 CQ=2

Q: The minimum information to find a line equation is : *

A: Given problem is :

Q: Find the equation of the line tangent to a circle with center at (3,2) and radius 5 at the point…

A: The center of the circle is:  (h, k) = (3, 2) Radius of the circle is:  r = 5 Now we have to find…

Q: Find the points where the line y=x4 intersects a circle of radius 2 centered at the origin. Give…

A:

Q: What is the equation of a circle with its center at (0,–2) and passing through the point (3, –5)?

A: Given,          The equation of a circle with its center at 0,-2 and passing through the…

Q: Find the points where the line y=−3xy=-3x intersects a circle of radius 2 centered at the origin.…

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Q: (a) The curve with equation 2 y 3 + y2 - y 5   = x 4 -2x3  +x 2  has been likened to a bouncing…

A:

Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

A:

Q: =12 Sho

A: Straight line: The slope intercept form is y=mx+c Where m=slope. c is y-intercept.

Q: Find the equation of locus of a point which is at distance 5 from A(4,-3)

A:

Q: XIV. Give equation of straight line through point (1,3,-2) perpendicular to z = Зх-2y +4.

A: Given z=3x−2y+4 and point is x0,y0,z0=1,3,−2 We have to find the equation of straight line through…

Q: Find the point (s) on x = 3 - y2 that are closest to point A = (1,0).

A: Given: x = 3 - y2 and point A = (1, 0)

Q: Find the equation of the tangent line to the ellipse 25x2+ y2 = 109 at the point (2, 3

A:

Q: equation of the curve that passes through the point (0, 6) and whose slope at (x, y) is x/y.

A:

Q: 17. Passes through the point (2, 1) and is perpendicular to y = -x+ 3.

A:

Q: Find an equation of the line through the point (1, 2) that is perpendicular to th = --x +3 Select…

A: The given question is solved below.

Q: 3. What is the equation of the line that passes through point (-3,-1) and is perpendicular to the…

A: Given that: The given equation of the line is y=-13x+5 and the given point is -3, -1 So, we have to…

Q: 2. Find the equation of line pass through the origin and parallel the line with equation y = 2.

A: Point (0,0), equation, y=2

Q: 4 Construct line AB whose equation is given: y =-,+5 %3D Graph the y-intercept first; then graph a…

A: Giveny=-43x+5

Q: The point (0, 1) has the distance from the line defined by y = -2x – 1

A: Solve for distance

Q: (2,1) From the graph, find the midpoint of the line segment with endpoints of (- 2, 1) and (4, 3).…

A:

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13= 0 in which the tangent…

A:

Q: Find the distance between point (5,-1) and line x=3y-12.

A: Given: The point (5, -1) and the line  x = 3y -12. To find: The distance between the given point and…

Q: Express point P- 3,- into Cartesian coordinates with an aid of a suitable diagram.

A:

Q: Find the points where the line y=−x/4 intersects a circle of radius 8 centered at the origin. Give…

A:

Q: Determine the equation of the line passing through the point (3,22) which minimizes the area of the…

A: This question is based on application of Derivative. The two-point form of a line passing through…

Q: Find the points of intersection of the circle C of radius 3 centered at (-1, -2) and the line L with…

A: Want to find:                         the points of intersection of the circle C of radius 3…

Q: Find an equation for the set of all points (r, y, z) equidistant from point 10.) (1,0, 2) and the…

A:

Q: The curve y=ax²+bx+c passes through the point (2,28) and is tangent to the line y=4x at the origin.…

A: Given, y=ax2+bx+c

Q: Write down equation of the line in space passing through the points Po(1,0,0) and P (0, 1, 1).

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Q: Point P (0,2) is the point of intersection of y axis and perpendicular bisector of line segment…

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Q: Find the equations of the tangent lines to the circle x2 + y2 = 9 which pass through the point (-7,…

A:

Q: Does this curve go through the point (-1, 1, -1)?

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Q: What point on the curve y = x is closest to the point (5, 0)?

A:

Q: Find the distance of the point (2, 6, 4)  from the x-axis by two methods

A: To find the distance between the point.

Q: Point A is located at (-1,-5). The midpoint of line segment AB is point C (2, 3). What are the…

A:

Q: The y-axis and the line x = c are the banks of a river whose current has uniform speed a in the…

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Q: At point (1,y), what is y?

A: Note:- If two points is given in Cartesian form like  (2,5)  Then  x=2 and y=5 Means first one is…

Q: 4. Find the member of the curve whose slope at any point is 4y point (3, 4) and passes through the

A: Note: As they are different questions, as per our company guidelines we are supposed to answer the…