The equation of the ellipse whose axes are along the coordinate axes, vertices are (±5, 0) are foci at (±4, 0), is
Let the equation of the required ellipse be
The coordinates of its vertices and foci are (±a, 0) and (±ae, 0) respectively.
Substituting the values of a2 and b2 in (i), we get , which is the equation of the required ellipse.
The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q. If M is the mid-point of the line segment PQ then the locus of M intersects the latusrectums of the given ellipse at the points
The equation represents an ellipse, if
The curve with parametric equations
The curve represented by
Length of the major axis of the ellipse , is
The length of the axes of the conic 9x2 + 4y2 – 6x + 4y + 1 = 0 are
The eccentricity of the ellipse
If the eccentricities of the two ellipse
are equal, then the value , is
The curve represented by the equation
The equation of the ellipse whose axes are along the coordinate axes, vertices are (0, ±10) and eccentricity e = 4/5, is