Question

Find the equation of a circle whose diameter is the portion of the line 3x+4y =14 intercepted by the
lines x-y = 0 and 11x-4y = 0 ​

Answer 1

Solution

We have,

Equation of intercepted line is

$3x + 4y - - eq.1$

Equation of lines diameter

$x - y = 0 - - eq.2$

$11x - 4y = 0 - - eq.3$

from equation 1 and 2 we get,

(x1, y1)=7

From equation (1) and (3) to, and we get,

(x2, y2)=(1,11/4)

So, equation of circle if given diameter points

Then,

(x1-x2diameter points

Then,

(x-x1)(x-x2)+(y-y1)(y-y2)=0

(x-7)(x-1)+(y-7)(y-11/4)

x²-x-7x+7+y²-11/4y-7y+77/4=0

x²+y²-8x-39/4y+105/4=0

4x²+4y²-8x-39y+105=0

Hence, this is the answer.

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