Basics of Ellipse

IMPORTANT

Basics of Ellipse: Overview

This topic covers concepts such as Ellipse, Ellipse as a Conic Section, Ellipse as Locus of Point Having Constant Ratio between Distances from a Point and a Line, Second Degree General Equation and Ellipse, Standard Equation of Ellipse, etc.

Important Questions on Basics of Ellipse

MEDIUM
IMPORTANT

Find the eccentricity, foci and directrices of the ellipse:

4x2+y2-8x+2y+1=0.

HARD
IMPORTANT

Find the length of the focal chord of the ellipse x242+y232=1, which is inclined to the major axis at angle 60°.

HARD
IMPORTANT

Find the length of the focal chord of the ellipse x232+y222=1, which is inclined to the major axis at angle 60°.

HARD
IMPORTANT

Find the length of the focal chord of the ellipse x232+y222=1, which is inclined to the major axis at angle 30°.

HARD
IMPORTANT

Find the length of the focal chord of the ellipse x232+y222=1, which is inclined to the major axis at angle 45°.

HARD
IMPORTANT

Suppose that the chord joining the points θ1 and θ2 on the ellipse x2a2+y2b2=1 intersects the major-axis at (k,0). Show that tanθ12tanθ22=k-ak+a.

HARD
IMPORTANT

Suppose that the chord joining the points θ1 and θ2 on the ellipse x2a2+y2b2=1 intersects the major-axis at (h,0). Show that tanθ12tanθ22=h-ah+a.

HARD
IMPORTANT

The equation of the chord joining two points having eccentric angles θ and ϕ an the ellipse is 

HARD
IMPORTANT

If α and β are the eccentric angles of the extremities of a focal chord of an ellipse x2a2+y2b2=1(a>b). Then the eccentricity of the ellipse.

HARD
IMPORTANT

If θ1,θ2 are the eccentric angles of the extremities of a focal chord of an ellipse x2a2+y2b2=1(a>b) and its eccentricity is e. Then show that ecosθ1+θ22=cosθ1-θ22.

MEDIUM
IMPORTANT

Find the equation of the ellipse whose axes are parallel to the coordinate axes and centre is 1,1 and passes through two given points (4,3) and (-1,4).

MEDIUM
IMPORTANT

Draw the following standard equation of an ellipse x249+y216=1 using coordinates of vertices, coordinates of foci and equation of directrices. Then find the eccentricity of the ellipse.

MEDIUM
IMPORTANT

Draw the following standard equation of an ellipse x2144+y281=1 using coordinates of vertices, coordinates of foci and equation of directrices. Then find the eccentricity of the ellipse.

MEDIUM
IMPORTANT

Draw the following standard equation of an ellipse x225+y216=1 using coordinates of vertices, coordinates of foci and equation of directrices. Then find the eccentricity of the ellipse.

MEDIUM
IMPORTANT

Draw the following standard equation of an ellipse x225+y29=1 using coordinates of vertices and foci. Then find the eccentricity of the ellipse.

MEDIUM
IMPORTANT

Draw the following standard equation of an ellipse x216+y29=1 using coordinates of vertices and foci. Then find the eccentricity of the ellipse.

HARD
IMPORTANT

Find the equation of ellipse with centre at origin, major axis on the x-axis and satisfying 
Length of major axis =8 and eccentricity=12

MEDIUM
IMPORTANT

Find the equation of ellipse having foci at (±3,0), passing through (4,1).

MEDIUM
IMPORTANT

Find the equation of ellipse having foci at (0,±4), e=45.

HARD
IMPORTANT

Find the equation of ellipse satisfying that the vertices at (0,±10),e=45