Question

Find the coordinates of the point of intersection of tangents at the points where x + 4y –14 = 0 meets the circle x2 + y2 – 2x + 3y – 5 = 0.

Answer 1

Equation of the given circle is

x2 + y2 – 2x + 3y – 5 = 0

polar of P(x1, y1) is

Equation of QR is x + 4y – 14 = 0 –––(2)

Comparing (1) and (2)

y1 = 9/38

∴ Co- ordinates of p are (109/76,9/38)