## Question

For what value of λ does the line *y* = 2*x* + λ touches the hyperbola

### Solution

Equation of hyperbola is

Comparing this with we get *a*^{2} = 9, *b*^{2} = 16.

and comparing this line *y* = 2*x* + λ with *y* = *mx* + *c*

If the line *y* = 2*x* + λ touches the hyperbola

.

#### SIMILAR QUESTIONS

To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci.

Find the equation of the hyperbola whose directrix is 2*x* + *y* = 1, focus (1, 2) and eccentricity .

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

Find the equation of the hyperbola whose foci are (6, 4) and (–4, 4) and eccentricity is 2.

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

The foci of a hyperbola coincide with the foci of the ellipse . Find the equation of the hyperbola if its eccentricity is 2.

Find the equation of the tangent to the hyperbola *x*^{2} – 4*y*^{2} = 36 which is perpendicular to the line *x* – *y* + 4 = 0.

Find the equation and the length of the common tangents to hyperbola

Find the locus of the foot of perpendicular from the centre upon any normal to the hyperbola .

Find the locus of the mid-points of the chords of the hyperbola which subtend a right angle at the origin.