A house on a hill is enclosed by a circular fence with center at the front door. The fence is made of wooden boards of uniform height. If we use a coordinate system with origin at the center of the circle, then the fence can be described as x² + y² = 80. Suppose the elevation at any point on the base of the fence relative to the elevation of the front door is given by 4x - 2y. What is the location (point) of minimum elevation of this fence?

Q: Kelly is plotting points on a graph to make a rectangle. So far she has done (1,1) (1,5) and (3,1).…

A: Lets try to plot the graph first, then we will solve the problem.

Q: Consider the following equation of a circle written in expanded form. x² + y² + 4x+10y = - 4 Whic…

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Q: Find the equation of the smaller circle that touches the circles x2 +y2=1  and passes through the…

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Q: nd the condit. on if the circle whose equation a x² + y² + c² = 2ax = 0 and x² + y² + c² = 2b y = 0…

A: The two circles are x2+y2+c2=2ax=0 and x2+y2+c2=2by=0.centers:C1(a,0),C2(0,b)radii:r1=a2=c2,r2=b2-c2

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A: When we have a three-dimensional space-XYZ. We take a point in the space that is represented by (x,…

Q: 1.- (-3,-2) 2.- (3, 3) 3.- (1,--5). 4. (4,-4) 4 5.-(-3,--5) 6.- (3,-5) 7.+ (-2,-4) 8. (1, -3)

A: rectangular coordinate are (x,y)

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A: Centre= (5,7) Radius= 2

Q: - If the equation px² + (2−q)xy + 3y² − 6qx +3 e presents a circle then find the values of pand q.

A: Let the equation of the circle be           x2+y2+2gx+2fy+c=0        .....(1)If eq (1) passes…

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A:

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A: We are given : 2x2+3xy-4y2-3y+1=0 Plotting the graph, we have : This graph is a Hyperbola.

Q: Find an equation for a circle of radius 4 and center at the point (0,-2).

A: Given: For a circle,                           radius, r = 4 And            center, (h, k) = (0,-2)

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A: Drone 1 :  y = -0.2x2 + 2x…