Start Free Mock LoginAlready registered? Login here

Mathematics - Hyperbola Question with Solution | TestHub

MathematicsHyperbolaTangents & NormalsHard3 minQB

MathematicsHardnumerical

A common tangent to $y^{2} = 8 x$ and $x^{2} - y^{2} /3 = 1$ , together with the parabola's directrix, forms a triangle. Find its area.

Answer:

4.50

Solution:

A parabola tangent is $y = m x + 2/ m$ . Hyperbola tangency gives $4/ m^{2} = m^{2} - 3$ , hence $m = \pm 2$ . The triangle has area $\frac{1}{2} \cdot 6 \cdot \frac{3}{2} = 9/2$ .

Stream:JEESubject:MathematicsTopic:HyperbolaSubtopic:Tangents & Normals

⏱ 3mℹ️ Source: QB

Doubts & Discussion

Loading discussions...