Question

Equation of
tangent to the
circle x square plus y square= 25.
through (-2, 11) is​

Answer 1

Answer:

solved

Step-by-step explanation:

the distance of tangent from the center of circle is equal to the radius of circle.

So, let the equation of tangent be y=mx+c

Mx-y+c=0

So distance of this line from the center (0,0) of given circle is

5=|m(0)−(0)+c| / √m²+1

5√m²+1 =c

Now on squaring both sides

25(m²+1)=c2      ...............(1)

Now as given this tangent is passes through (-2,11) so this will satisfied this equation

Y=mx+c

11x=-2m+c

C=11+2m……………(2)

25m²+25= 4m²+121+44 m

225m²−44m−96=0

So from this we will find the two values of ‘m’

m=24/7, - 4/3

For different values of m we will get different value of c with the help of equation (2)

So we will get the following equations

Y=24/7x+48/7+11

Y=-4/3x-8/3+11

comments:

Beautiful problem