## Question

Determiner the equation of common tangents to the hyperbola and .

### Solution

Tangents to ... (1)

Tangents to ... (2)

As (1) and (2) are same, *m*_{1} = *m*_{2} and *a*^{2}*m*_{1}^{2} – *b*_{1}^{2}*m*_{1}^{2} + *a*^{2}

⇒ (*a*^{2} + *b*^{2}) *m*_{1}^{2} = *a*^{2} + *b*^{2}

.

#### SIMILAR QUESTIONS

If values of m for which the line touches the hyperbola 16x^{2} – 9y^{2 }= 144 are the roots of the equation x^{2} –(a + b)x – 4 = 0, then value of (a + b) is equal to –

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From a point on the line y = x + c, c(parameter), tangents are drawn to the hyperbola such that chords of contact pass through a fixed point (x_{1}, y_{1}). Then is equal to –

If the portion of the asymptotes between centre and the tangent at the vertex of hyperbola in the third quadrant is cut by the line being parameter, then –

Find the eccentricity of the hyperbola whose latus rectum is half of its transverse axis.

For what value of *c* does not line *y* = 2*x* + *c* touches the hyperbola 16*x*^{2} – 9*y*^{2} = 144?

Find the locus of the mid-pints of the chords of the circle *x*^{2} – *y*^{2} = 16, which are tangent to the hyperbola 9*x*^{2} – 16*y*^{2} = 144.

Find the locus of the poles of the normal of the hyperbola .

Obtain the equation of a hyperbola with coordinate axes as principal axes given that the distance of one of its vertices from the foci are 9 and 1 units.