Home
Class 12
MATHS
Find the equation of the tangent at the ...

Find the equation of the tangent at the endpoints of the diameter of circle `(x-a)^2+(y-b)^2=r^2` which is inclined at an angle `theta` with the positive x-axis.

Text Solution

Verified by Experts

Diameter makes an angle `theta` with x-axis.
So, the slope of diameter is `tan theta`

Let this diameter meet the circle at points A and B.
Thus, the coordinates of A and B are given by `(a+- r cos theta, b +- r sin theta)`
Therefore, equations of tangents at points A and B are given by
`(x-a)(a+-r cos theta-a) +(y-b)(b+-r sin theta -b)=r^(2)`
or `+-(x-a)cos theta +- r(y-b) sin theta =r`
or `(x-a)cos theta +(y-b) sin theta = +- r `
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Find the equation of the tangent at t =2 to the parabola y^(2) = 8x .

Find the equation of the tangent and normal to the circle x^(2)+y^(2)=25 at P(-3,4)

If theta is the angle between the lines given by the equation 6x^2+5x y-4y^2+7x+13 y-3=0 , then find the equation of the line passing through the point of intersection of these lines and making an angle theta with the positive x-axis.

Find the equation of the tangent to the curve (1+x^2)y=2-x , where it crosses the x-axis.

Find the equation of the tangent to the curve (1+x^2)y=2-x , where it crosses the x-axis.

Find the angle between the two tangents from the origin to the circle (x-7)^2+(y+1)^2=25

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

Find the equations of the tangent and normal to the circle x^(2)+y^(2)=169 at the point (5,12) .