Class XI Maths Conic Section 4 - Ellipse

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Question 1

If the axes of an ellipse coincide with the co-ordinate axes and it passes through the point (4, – 1) and touches the line x + 4y – 10 = 0 then its equation is -

• A+ = 1
• B– = 1
• C+ = 1
• DNone of these

Question 2

The condition that the line lx + my = n may be a normal to the ellipse + = 1 is

• A= 1
• B = 1
• C= 2
• DNone of these

Question 3

Let L = 0 is a tangent to ellipse + = 1 and S, S′be its foci. If length of perpendicular from S on L = 0 is 2 then length of perpendicular from S′ on L = 0 is

• A3
• B
• C2
• Dnone

Question 4

If there are exactly two points on the ellipse whose distance from the centre is , then the eccentricity of the ellipse is

• A
• B
• C
• Dnone of these

Question 5

If the ellipse intersect at A, B, C, D, then

• AA, B, C and D are concyclic
• BA, B, C and D are the vertices of rectangle
• CA, B, C and D are the vertices of a square
• Dall of the above

Question 6

The locus of the middle points of the portion of the tangents of the ellipse included between the axis is the curve

• A
• B
• Ca²x² + b²y² = 4
• Db²x² + a²y² = 4

Question 7

The locus of the middle points of the portion of the tangents of the ellipse included between the axis is the curve

• A
• B
• Ca²x² + b²y² = 4
• Db²x² + a²y² = 4

Question 8

The tangent is drawn at (a cos θ, b sin θ) on the ellipse b²x² + a²y² – a²b² = 0. It meets the auxiliary circle of the ellipse in two points. If the angle subtended by the chord joining two points at the centre of ellipse is π/2, then the eccentricity of the ellipse is

• A
• B
• C
• D

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