Paragraph: The circle x 2 + y 2 − 8 x = 0 and hyperbola 9 x 2 − 4 y 2 = 1 intersect at the points A and B . Question: Equation of a common tangent with positive slope to the circle as well as to t

Question

Paragraph: The circle x 2 + y 2 − 8 x = 0 and hyperbola 9 x 2 ​ − 4 y 2 ​ = 1 intersect at the points A and B . Question: Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

TestHub · Accepted Answer

Equation of tangent to hyperbola having slope m is y = m x + 9 m 2 − 4 ​ Equation of tangent to circle is y = m ( x − 4 ) + 16 m 2 + 16 ​ Eqs. (i) and (ii) will be identical for m = 5 ​ 2 ​ satisfy. ∴ Equation of common tangent is 2 x − 5 ​ y + 4 = 0

Mathematics - Hyperbola Question with Solution | TestHub

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