Question

What will be the length of a tangent from the point (7, 2) to the circle 2x^2 + 2y^2 + 5 x + y = 15?

(a) 10 units

(b) 8 units

(c) 6 units

(d) 4 units

I had been asked this question in homework.

My enquiry is from Calculus Application in chapter Application of Calculus of Mathematics – Class 12

Answer 1

Right option is (b) 8 units

Explanation: The given equation of the circle is,

2x^2 + 2y^2 + 5 x + y – 15 = 0

Or x^2 + y^2 + 5/2 x + y/2 – 15/2 = 0 ………..(1)

The required length of the tangent drawn from the point (7, 2) to the circle (1) is,

√(7^2 + 2^2 + 5/2 (7) + 1/2 – 15/2)

= √(49 + 4 + 35/2 + 1 – 15/2)

= √64

= 8 units.