## Question

The equation of normal to the rectangular hyperbola xy = 4 at the point P on the hyperbola which is parallel to the line

2x – y = 5 is –

### Solution

Slope of the normal to the rectangular hyperbola xy = 4 is m = t^{2} = 2 and 2x – y = 5 has slope = 2.

Equation of the normal is

⇒ ty – 2 = 2tx – 4t^{2}

⇒ 2tx – ty + 2 – 4t^{2}

#### SIMILAR QUESTIONS

Sa circle with fixed center (3h, 3k) and of variable radius cuts the rectangular hyperbola x^{2} – y^{2} = 9a^{2} at the points A, B, C, D. The locus of the centroid of the triangle ABC is given by

If PQ is a double ordinate of the hyperbola such the OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies –

A rectangular hyperbola passes through the points A(1, 1), B(1, 5) and C(3, 1). The equation of normal to the hyperbola at A(1, 1) is –

If a variable line which is a chord of the hyperbola subtends a right angle at the centre of the hyperbola then it always touches a fixed circle whose radius is –

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 –

A tangent to the hyperbola meets ellipse x^{2} + 4y^{2} = 4 in two distinct points. Then the locus of midpoint of this chord is –

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?