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 Q 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

Let P be (x₁, y₁), then

x₁² + y₁² + 6x₁+ 6y₁ – 2 = 0 ....(i)

& equation of tangent at P is

xx₁ + yy₁ + 3 (x + x₁) + 3(y + y₁) –2 = 0 ….(ii)

Now Q is (0, 3)

\ (ii) passes through (0, 3), we have

Ž 3y₁ + 3x₁ + 9 + 3y₁ –2 = 0

Ž 3x₁ + 6y₁ + 7 = 0

Now,

PQ² = (x₁ – 0)² + (y₁ – 3)²

= 2 (3x₁ + 6y₁ ) + 9 = 25

PQ = 5