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

Category: QuestionsWhat will be the length of a tangent from the point (7, 2) to the circle 2x^2 + 2y^2 + 5 x + y = 15?
Editor">Editor Staff asked 11 months ago

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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

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.