Question

If the tangent at the point P on the circle x² + y² + 6x + 6y = 2 meets the straight line 5x – 2y+6= 0 at a point on the y-axis, then the length of PQ is

• A. 4
• B. 2$\sqrt { 5 }$
• C. 5
• D. 3$\sqrt { 5 }$

Answer 1

Answer: (C)

5

Answer 2

The line 5x – 2y + 6 = 0 meets the y-axis at (0, 3). We have now to find the length of the tangent from Q (0, 3) to the given circle. Hence

PQ = $\sqrt { 0 + 3 ^ { 2 } + 0 + 6 \times 3 - 2 } = 5$