Question

Identify the equation for the line tangent to the circle x^2 + y^2 = 100 at the point (−6, 8).

Answer 1

The equation of tangent to the circle $x^{2} +y^{2} =100$ at the point  (-6,8) is -6x+8y=100.

Given the equation of circle $x^{2} +y^{2} =100$

and point at which the tangent meets the circle is (-6,8).

A tangent to a circle is basically a line at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of circle to the point P.

Linear equation looks like y=mx+c.

Tangent to a circle of equation $x^{2} +y^{2} =a^{2}$ at (z,t) is:

xz+ty=$a^{2}$.

We have to just put the values in the formula above to get the equation of tangent to the circle $x^{2} +y^{2} =100$  at (-6,8).

It will be as under:

x(-6)+y(8)=100

-6x+8y=100

Hence the equation of tangent to the circle at the point  (-6,8) is -6x+8y=100.

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