Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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

Sagot :

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

Given the equation of circle [tex]x^{2} +y^{2} =100[/tex]

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 [tex]x^{2} +y^{2} =a^{2}[/tex] at (z,t) is:

xz+ty=[tex]a^{2}[/tex].

We have to just put the values in the formula above to get the equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex]  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.

Learn more about tangent of circle at https://brainly.com/question/17040970

#SPJ1