Math, asked by bosssd02, 5 months ago

equation to the circle orthogonal to the two circles x² + y2 -4x -6y+11=0 and x²+y²-10x- 4y+21=0 and has 2x + 3y =7 as diameter is

Answers

Answered by shkulsum3

The equation of a circle with center (h, k) and radius r is given by (x - h)² + (y - k)² = r².

To find the equation of a circle orthogonal to two given circles, we can first find the intersection points of the two given circles.

The intersection points can be found by solving the system of equations formed by the two given circles' equations.

Let's call the center of the first circle (h1, k1) and radius r1 and the center of the second circle (h2, k2) and radius r2.

We know that 2x + 3y = 7 is the equation of the diameter that passes through the center of the circle we are trying to find the equation of.

So, we can find the center of the circle by solving the system of equations:

2x + 3y = 7 and (x - h1)² + (y - k1)² = r1²

(x - h2)² + (y - k2)² = r2²

Once we have the center (h, k) of the circle, we can use the distance formula to find the radius r.

Finally, the equation of the circle orthogonal to the two given circles and with 2x + 3y = 7 as diameter is (x - h)² + (y - k)² = r²