Experts please help in 16th question Q16 If a circle cut off - Maths -

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Experts please help in 16th question

Q16 If a circle cut off an intercept of 2 5 units
on the x-axis and its tangent at (3, 2) is parallel to y-axis then
find the equations of the circles

Zuhaib Ul Zamann · Accepted Answer

Dear student,
Let the equation of the circle bex2+y2+2gx+2fy+c=0So we haveFor x intercept y=0x2+2gx+c=0x=-2g±4g2-4c2x1=-g-g2-c,x2=-g+g2-cSo intercept length=x2-x1=2g2-cSo we have2g2-c=25g2-c=5c=g2-5       (A)Also tangent at (3,2) is3x+2y+g(x+3)+f(y+2)+c=0 is parallel to y-xaxisSo we haveCoefficient of y=0 i
e f+2=0f=-2Also as (3,2) lies on circle we have9+4+6g+4f+c=013-8+6g+c=05+6g+c=0From A we have5+6g+g2-5=0i
e g=0,-6If g=0 we have c=-5If g=-6 we have c=31So the circles are x2+y2-4y-5=0 and x2+y2-12x-4y+31=0Regards

Experts please help in 16th question...... Q16. If a circle cut off an intercept of 2 5 units on the x-axis and its tangent at (3, 2) is parallel to y-axis. then find the equations of the circles.

Experts please help in 16th question......

Q16. If a circle cut off an intercept of $2 \sqrt{5}$ units on the x-axis and its tangent at (3, 2) is parallel to y-axis. then find the equations of the circles.