Standard equation of hyperbola and mixed ellipse questionsHard

Circle Tangent and Hyperbola Properties

Let the circle C touch the line x – y + 1 = 0, have the centre on the positive x-axis, and cut off a chord of length $\frac{4}{{\sqrt {13} }}$ along the line –3x + 2y = 1. Let H be the hyperbola $\frac{{{x^2}}}{{{\alpha ^2}}} - \frac{{{y^2}}}{{{\beta ^2}}} = 1$ , whose one of the foci is the centre of C and the length of the transverse axis is the diameter of C. Then 2α² + 3β² is equal to ________

Ask about this question

Standard equation of hyperbola and mixed ellipse questionsHard

Circle Tangent and Hyperbola Properties

Ask about this question