Home
Class 12
MATHS
Find the equations of tangents to the ci...

Find the equations of tangents to the circle `x^2+y^2-22 x-4y+25=0` which are perpendicular to the line `5x+12 y+8=0`

Text Solution

Verified by Experts

The correct Answer is:
`12x-5y+8=0` and `12x-5y=252`
Given circle is `x^(2)+y^(2)-22x-4y+25=0`.
Centre is (11,2) and radius is `sqrt(121+4-25)=10`
Equation of line perpendicular to `5x+12y+8=0` is `12x-5y+k=0` .
If this line touches the circle, then distance of the centre of the circle from the line radius.
`:. |(12(11)-5(2)+k)/(sqrt(144+25))|=10`
`implies |k+122|=130`
`implies k=8` or `-252`
Hence equations of tangents are
`12x+5y+8=0` and `12x-5y=252`.
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Find the equations of the tangents drawn to the curve y^2-2x^3-4y+8=0.

Find the equations of the tangents to the circle x^2+y^2-6x+4y=12 which are parallel to the straight line 4x+3y+5=0

Find the equation of tangent to the circle x^(2) + y^(2) + 2x -3y -8 = 0 at (2,3)

Find the equation of tangent to the conic x^2-y^2-8x+2y+11=0 at (2,1)

Find the equation of tangents to hyperbola x^(2)-y^(2)-4x-2y=0 having slope 2.

Find the equation of tangents to circle x^(2)+y^(2)-2x+4y-4=0 drawn from point P(2,3).

Find the equation of the tangent line to the curve y = x^(2) – 2x +7 which is (a) parallel to the line 2x – y + 9 = 0 (b) perpendicular to the line 5y – 15x = 13.

Find the equation of the normals to the circle x^2+y^2-8x-2y+12=0 at the point whose ordinate is -1

Find the equations of the tangents to the curve y=1+x^(3) for which the tangent is orthogonal with the line x + 12y = 12.