Home
Class 12
MATHS
The slopes of the common tangents of the...

The slopes of the common tangents of the ellipse `(x^2)/4+(y^2)/1=1` and the circle `x^2+y^2=3` are `+-1` (b) `+-sqrt(2)` (c) `+-sqrt(3)` (d) none of these

A

`+-1`

B

`+-sqrt(2)`

C

`+-sqrt(3)`

D

none of these

Text Solution

Verified by Experts

Let m be the slop of the common tanent .Then,
`+-sqrt(3)sqrt(1+m^(2))=+-sqrt(4m^(2)+1)`
or `3+2m^(2)=4m^(2)+1`
or `m^(2)=2`
or `m=+-sqrt(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the common tangents to the hyperbola x^(2)-2y^(2)=4 and the circle x^(2)+y^(2)=1

Find the slope of a common tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and a concentric circle of radius rdot

The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the point (1,3) is

The line y=x+lambda is tangent to the ellipse 2x^(2)+3y^(2)=1 , then lambda is-

Find the equation of the tangent to the ellipse x^2/a^2+y^2/b^2=1 at (x= 1,y= 1) .

The slope of the tangent to the curve (y-x^(5))^(2)=x(1+x^(2))^(2) at the point (1, 3) is

The equation of the common tangent touching the circle (x-3)^2+y^2=9 and the parabola y^2=4x above the x-axis is sqrt(3)y=3x+1 (b) sqrt(3)y=-(x+3) (C) sqrt(3)y=x+3 (d) sqrt(3)y=-(3x-1)

How many tangents to the circle x^2 + y^2 = 3 are normal to the ellipse x^2/9+y^2/4=1?

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

If tan^(-1)((a+x)/a)+tan^(-1)((a-x)/a)=pi/6,then x^2= 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these