## Question

The equation of common tangent to the curves *y*^{2} = 8*x* and *xy* = –1 is

### Solution

*y* = *x* + 2

*y*^{2} = 8*x* = 4*ax*

… (3)

(3) is also tangent for curve (2), Now (2) and (3)

For common tangent this eq. will have one root.

*B*^{2} – 4*AC* = 0

So put this to get *y* = *x* + 2

#### SIMILAR QUESTIONS

The pints of intersection of the two ellipse *x*^{2} + 2*y*^{2} – 6*x* – 12*y* + 23 = 0 and 4*x*^{2} + 2*y*^{2} – 20*x* – 12*y* + 35 = 0.

The tangent at any point *P** *of the hyperbola makes an intercept of length *p* between the point of contact and the transverse axis of the hyperbola, *p*_{1}, *p*_{2} are the lengths of the perpendiculars drawn from the foci on the normal at *P*, then

The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola *y*^{2} = 8*x*, is

The locus of a point whose some of the distance from the origin and the line *x* = 2 is 4 units, is

The length of the subnormal to the parabola *y*^{2} = 4*ax* at any point is equal to

The slope of the normal at the point (*at*^{2}, 2*at*) of parabola *y*^{2} = 4*ax* is

Equation of locus of a point whose distance from point (*a*, 0) is equal to its distance from y-axis is

Through the vertex *O* of parabola *y*^{2} = 4*x*, chords *OP* and *OQ* are drawn at right angles to one another. The locus of the middle point of *PQ *is

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola *y*^{2} = 4*ax* is another parabola with directrix

From the point (–1, 2) tangent lines are drawn to the parabola *y*^{2} = 4*x*, then the equation of chord of contact is