If a line y = m x + c , is a tangent to the circle x - 3 2 + y 2 = 1 , and it is perpendicular to a line L 1 , where L 1 is the tangent to the circle x 2 + y 2 = 1 , at the point 1 2 ,   1 2 , then

Question

If a line y = m x + c , is a tangent to the circle x - 3 2 + y 2 = 1 , and it is perpendicular to a line L 1 , where L 1 is the tangent to the circle x 2 + y 2 = 1 , at the point 1 2 , &#8201; 1 2 , then

Aicharya · Accepted Answer

Slope of tangent to x 2 + y 2 = 1 at 1 2 , 1 2 x 2 + y 2 = 1 2 x + 2 y y ' = 0 y ' = - x y = - 1 Given that, y = m x + c , is perpendicular to L 1 , So, m = 1 &#160; &#8658; y = x + c Now distance of 3 , 0 from y = x + c is c + 3 2 = 1 c 2 + 6 c + 9 = 2 c 2 + 6 c + 7 = 0 .

If a line y = m x + c , is a tangent to the circle x - 3 2 + y 2 = 1 , and it is perpendicular to a line L 1…

Solution