of the chord of contact of the tangents drawn from a point on the circle x² + y² = a² to he circle x² + y² = 6² touches the circle x² + y² = ², then prove that a,b and care in GP.

Q: Use the Theorem of Pythagoras to find the length of the line segment y = 3xfrom (1,3) to (2,6), and…

A:

Q: Let the triangle ABC and A ', B', C ', the intersections of the tangents to its circumscribed circle…

A:

Q: 2x +3K Zx2 - 4x + 13

A:

Q: Show that the equation of a circle passing through the origin and having intercepts a and b on real…

A:

Q: A circle with center at the origin and radius equal to a meets the axis of x at A and B. P(a) and…

A: The coordinates of A are (-a,0) and that of P are (a cos α,a sin α)  Therefore,the equation of AP…

Q: If the lines 3x-4y+4=0 and 6x-8y-7=0 are tangents to a circle then find the radius of the circle.…

A: The diameter of circle is the perpendicular distance between the parallel lines (tangents) 3x-4y+4=0…

Q: OA, OB and OC, with O as the origin, are three mutually perpendicular lines whose direction cosines…

A:

Q: Use the Distance Formula to show that the circle with center (0, 0) and radius length r has the…

A: Given: x2+y2=r2 Formula used: OA=x-02+y-02

Q: Let ∆ABC be a triangle. (a) Prove that B’ lies in the interior of AC if and only if ∠BAC and ∠ACB…

A:

Q: Find the range of values of m for which the line y=mx+2 cuts the circle x\power{2}+y\power{2}=1 at…

A: The length of the perpendicular from the center (0, 0) to the line is                   21+m2

Q: If the radical axis of the circles x² + y² + 2 gx + 2 fy+c= 0 and 2x² + 2y² +3x+8y +2c=0 touches the…

A: The radical axis of the given circles             x2+y2+2gx+2fy+c=0and      x2+y2+(3/2)x+4y+c=0 is…

Q: Find the distance from the point (0,0,−9) to the line x = t, y = - 3t, and z = t. The distance is…

A:

Q: If a circle passes through the point (0,0),(a,0) and (0,b),then find its center. Prove that for all…

A: There are many parts of question but not metioned a particular question so i am solving all portion…

Q: Evaluate ry dr +r dy, where C is the positively oriented triangle enclosed by the lines y = I=0 and…

A:

Q: If the tangents are drawn to the circle x2 + y2 = 12 at the point where it meets the circle x2 +…

A: Given that               x2+y2=12              x2+y2-5x+3y-2=0Let (h, k) be the point of…

Q: The lengths of the tangents from P(1, -1) and (3, 3) to a circle are √2 and √6, respectively. Then,…

A: Let the circle be x2+y2+2gx+2fy+c=0.Let the tangents from points P(1,-1), Q(3,3) and R(-1,-5) touch…

Q: if p� and q� are on the unit circle in the xy��-plane, then p×q=r⎛⎝⎜001⎞⎠⎟�×�=�(001)  where r� runs…

A: The objective of the question is to understand the relationship between two points on the unit…

Q: If a circle passes through the point (0,0),(a,0) and (0,6), then find its center.

A:

Q: B. Find the line through the point p(1,4) with an inclination V3

A:

Q: AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of…

A: Given in a circle of radius r, there are two chords AB and AC such that AB=2AC. Also, the distance…

Q: 3. Use the distance formula to prove that the point (4,2) is on the parabola x = Sy. Prenared hu

A:

Q: Compute . Z+1 dz, where C1 is a part of a circle with r = 3, and 0<0< %3D

A:

Q: Determine the area of the triangle formed by the following lines (can assume a > 0).

A:

Q: a) Find the image of the following under W = Z² 4) The line x = 3 2 <y<3 2) The domain b) Let f(Z) =…

A:

Q: Find the locus of the centers of the circles x² + y²-2ax-2by- +2=0, where a and b are parameters, if…

A:

Q: Prove that the length of common chord of the two circles x + y² + 22x + c = (2² -c)(µ² +c) 2² + µ? O…

A: We will prove that the length of the common chord is the given term as following.

Q: A secant to two congruent circles, which is parallel to the line of centers OO', meets the first…

A:

Q: If the distances from the origin of the centers of three circl x² + y² + 2A₁x − c = 0, (i = 1, 2,…

A: The centers of the given circles are (-λi,0),(i=1,2,3).The distances from the origin of the centers…

Q: A variable circle passes through the point A(a, b) and touches the x - axis. Show that he other end…

A: A variable circle passes through the point A(a,b) and touches the x-axis, then we have to show that…

Q: A rod of length a unit slides on the x-axis and another rod of length b unit slides on the y-axis in…

A: Given: A rod of length a unit slides on the x-axis and another rod of length b unit slides on the…

Q: If a circle passes through the point (0, 0), (a, 0) and (0, b), then find its center. Prove that for…

A:

Q: 2. Let be the part of the circle x² + y² = 9 from (-3,0) to (0, 3) in the upper left quadrant.…

A:

Q: For what values of a and b is the 2x + y =b  line tangent tothe parabola y =ax2 when x =2?

A: Rewrite the equation of the tangent line as y=-2x+b and its slope is -2.