Home
Class 12
MATHS
Show that for all real p the line 2px+y ...

Show that for all real p the line `2px+y sqrt(1-p^(2))=1` touches a fixed ellipse . Find the ecentricity of this ellipse.

Text Solution

Verified by Experts

The correct Answer is:
`(sqrt(3))/(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Show that for all real values of 't' the line 2tx + ysqrt(1-t^2)=1 touches the ellipse.Find the eccentricity of the ellipse.

For all real p, the line 2px+ysqrt(1-p^(2))=1 touches a fixed ellipse whose axex are the coordinate axes The foci of the ellipse are

For all real p, the line 2px+ysqrt(1-p^(2))=1 touches a fixed ellipse whose axex are the coordinate axes The foci of the ellipse are

For all real p, the line 2px+ysqrt(1-p^(2))=1 touches a fixed ellipse whose axex are the coordinate axes The locus of the point of intersection of perpendicular tangent is

The line 2px+ysqrt(1-p^(2))=1(abs(p)lt1) for different values of p, touches a fixed ellipse whose exes are the coordinate axes. Q. The eccentricity of the ellipse is

Show that the line y= x + sqrt(5/6 touches the ellipse 2x^2 + 3y^2 = 1 . Find the coordinates of the point of contact.

If the line 3 x +4y =sqrt7 touches the ellipse 3x^2 +4y^2 = 1, then the point of contact is

If the line 2px+ysqrt(5-6p^(2))=1, p in [-sqrt(5)/(6),sqrt(5)/(6)] , always touches the standard ellipse. Then find the eccentricity of the standard ellipse.

Show that the line (x-2)costheta+(y-2)sintheta=1 touches a circle for all values of theta .Find the circle.

A circle whose diameter is major aixs of ellipe (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtbgt0) meets minor axis at point P. Ifthe orthocentre of DeltaPF_(1)F_(2) lies on ellipse where F_(1)and F_(2) are foci of ellipse , then find the eccenricity of the ellipse