Class XI Maths Conic Section 5 - Hyperbola

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Question 1

The point of intersection of two tangents of the hyperbola = 1, the product of whose slopes is c², lies on the curve -

• Ay² – b² = c²(x² + a²)
• By² + a² = c²(x² – b²)
• Cy² + b² = c²(x² – a²)
• Dy² – a² = c²(x² + b²)

Question 2

If AB is a double ordinate of the hyperbola –= 1 such that ΔOAB (O is the origin) is an equilateral triangle, then the eccentricity 'e' of the hyperbola satisfies -

• Ae >
• B1 < e <
• Ce =
• De >

Question 3

• AA–(i), B–(ii), C–(iii), D–(iv)
• BA–(iv), B–(iii), C–(ii), D–(i)
• CA–(ii), B–(i), C–(iv), D–(iii)
• DA–(iv), B–(i), C–(ii), D–(iii)

Question 4

Locus of point of intersection of perpendicular lines passing through the vertices of the hyperbola xy = 8 is

• Ax² + y² = 8
• Bx² + y² = 16
• Cx² + y² = 32
• Dx² + y² = 4

Question 5

If ax + by = 1 is tangent to the hyperbola = 1, then a² – b² equals to

• A
• Ba²e²
• Cb²e²
• Dnone of these

Question 6

If hyperbola = 1 passes through the focus of ellipse = 1 then eccentricity of hyperbola is -

• A
• B
• C
• DNone

Question 7

Tangent at any point on the hyperbola = 1 cut the axes at A and B respectively. If the rectangle OAPB (where O is origin) is completed then locus of point P is given by

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

Question 8

If any point on a hyperbola is (3 tanθ, 2 secθ) then eccentricity of the hyperbola is

• A
• B
• C
• Dnone of these

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