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 foci of the ellipse are

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

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 locus of the point of intersection of prependicular tangents of the ellipse is

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 lines (p+2q)x+(p-3q)y=p-q for different values of p&q passes trough the fixed point is:

An ellipse intersects the hyperbola 2x^2-2y^2 =1 orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then (a) the foci of ellipse are (+-1, 0) (b) equation of ellipse is x^2+ 2y^2 =2 (c) the foci of ellipse are (+-sqrt 2, 0) (d) equation of ellipse is (x^2 +y^2 =4)

Find the equation to the ellipse with axes as the axes of coordinates. foci are (pm 4,0) and e=1/3 ,

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.

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.