Home
Class 12
MATHS
The equation of a tangent to the hyperbo...

The equation of a tangent to the hyperbola `4x^(2)-5y^(2)=20` parallel to the line x-y=2 is

A

`x-y-3=0`

B

`x-y+9=0`

C

`x-y+1=0`

D

`x-y+7=0`

Text Solution

Verified by Experts

Given equation of hyperbola is
`4x^(2)-5y^(2)=20`
which can be rewritten as
` rArr (x^(2))/(5)-(y^(2))/(4)=1`
The line `x-y=2` has slope , `m=1`
`therefore` Slope of tangent parallel to this line = 1
We know equation of tangent to hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
having slope m is given by
`y=mx pm sqrt(a^(2)m^(2)-b^(2))`
Here, `a^(2)=5, b^(2)=4 and m=1`
` therefore` Required equation of tangent is
`rArr y=xpm sqrt(5-4)`
`rArr y=x pm 1 rArr x-ypm 1=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

The equation of a tangent to the hyperbola 3x^(2)-y^(2)=3 , parallel to the line y = 2x +4 is

Statement 1 : The equations of tangents to the hyperbola 2x^2-3y^2=6 which is parallel to the line y=3x+4 are y=3x-5 and y=3x+5. Statement 2 : For a given slope, two parallel tangents can be drawn to the hyperbola.

The tangent to the hyperbola 3x^(2)-y^(2)=3 parallel to 2x-y+4=0 is:

The equation of tangent to hyperbola 4x^2-5y^2=20 which is parallel to x-y=2 is (a) x-y+3=0 (b) x-y+1=0 (c) x-y=0 (d) x-y-3=0

Find the equations of the tangents: to the parabola 4x^(2)-y^(2)=64 which are parallel to 10x-3y+9=0 .

Find the equations of tangents to the hyperbola x^(2)/16 - y^(2)/64 =1 which are parallelto 10x -3y + 9=0

Find the equation of tangents to hyperbola x^(2)-y^(2)-4x-2y=0 having slope 2.

Find the equation of the normal to the circle x^2+y^2-2x=0 parallel to the line x+2y=3.

Tangents are drawn to the hyperbola x^(2)/9 - y^(2)/4 parallel to the straight line 2x - y= 1 . One of the points of contact of tangents on the hyperbola is

Find the equations of the tangent: to the parabola y^(2)=16x , parallel to 3x-2y+5=0