Question

Solve this it's important for me

Answer 1

Step-by-step explanation:

Questions

find the equation of the circle if the equation of two diameters are 2x + y = 6 and 3x + 2y = 4 the radius of circle is 6 ?

Formula

Equation of circle =

${(x - a)}^{2} + ( {y - b)}^{2} = {r}^{2}$

where ( a,b) are co-ordinate of axis where centre of circle lie and r is its radius

Solutions

Given

Equation of Diameter of circle

2x +y = 6

3x + 2y = 4

radius = 9

Now

on solving above equation we get

X = 8 and y = -1

since the point of intersection of any two diameter of a circle is its centre.Therefor co-ordinate of the centre of required circle are (8,-1) and its radius is 9 (given).

Hence ,it's equation

(X - 8)^2 + (y + 1)^2 = 9^2

x^2 - 16x + y^2 + 2y = 81 - 64 -1

x^2 + y^2 - 16x +2y - 16 = 0

:-)