## Question

The locus of a variable point whose distance from (–2, 0) is times its distance from the line , is

### Solution

Ellipse

= 45 ⇒ Ellipse.

#### SIMILAR QUESTIONS

If x = 9 is the chord of contact of the hyperbola *x*^{2} – *y*^{2} = 9, then the equation of the corresponding pair of triangle is.

Find the equations of tangents to the hyperbola *x*^{2} – 4*y* = 36 which are perpendicular to the line* x – y* + 4 = 0

Find the coordinates of foci, the eccentricity and latus rectum. Determine also the equation of its directrices for the hyperbola

4*x*^{2} – 9*y*^{2} =36.

Find the distance from *A*(4, 2) to the points in which the line 3*x* – 5*y *= 2 meets the hyperbola *xy *= 24. Are these points on the same side of *A*?

The asymptotes of the hyperbola makes an angle 60^{0} with x-axis. Write down the equation of determiner conjugate to the diameter *y* = 2*x*.

Two straight lines pass through the fixed points and have gradients whose product is *k* > 0. Show that the locus of the points of intersection of the lines is a hyperbola.

Find the equation of the triangles drawn from the point (–2, –1) to the hyperbola 2*x*^{2} – 3*y*^{2} = 6.

Find the range of ‘*a*’ for which two perpendicular tangents can be drawn to the hyperbola from any point outside the hyperbola

.

Find the hyperbola whose asymptotes are 2*x – y* = 3 and 3*x + y* – 7 = 0 and which passes through the point (1, 1).

A variable straight line of slope 4 intersects the hyperbola *xy* = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is