Hyperbola

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What is the length of the conjugate axis of a hyperbola?

2a

2ae

a(e - 1)

2b (correct)

What is the equation of the transverse axis of a hyperbola?

BB' = 2b

x = ae

AA' = 2a (correct)

y = 2b

What is the relation between the semi-conjugate axis and the eccentricity of a hyperbola?

b = a/e

b = a(e - 1) (correct)

b = a(e + 1)

b = ae

What is the length of the latus rectum of a hyperbola?

2a(e^2 - 1) Signup and view all the answers

What is the equation of a directrix of a hyperbola?

x = -ae Signup and view all the answers

The product of the slopes of CP, CQ, CR and CS is equal to?

-1 Signup and view all the answers

If a circle cuts a rectangular hyperbola in A, B, C and D, and the parameters of these four points be t1, t2, t3 and t4 respectively, then what is the value of t1t2t3t4?

-1 Signup and view all the answers

What is the condition for a point to divide a line segment in the ratio 1:2?

16x^2 + 10xy + y^2 = 2 Signup and view all the answers

What is the relationship between the coordinates of P, Q, R and S, where t1, t2, t3 and t4 are the parameters of the points P, Q, R and S respectively?

P(ct1, t1), Q(ct2, t2), R(ct3, t3), S(ct4, t4) Signup and view all the answers

What is the relationship between H and D, where H is the orthocentre of ΔABC and D is a point on the rectangular hyperbola?

H and D are the extremities of a diagonal of the rectangular hyperbola Signup and view all the answers

What is the condition for a pair of straight lines?

abc + 2fgh - af^2 - bg^2 - ch^2 = 0 Signup and view all the answers

What is the eccentricity of a rectangular hyperbola?

2 Signup and view all the answers

What is the general equation of a rectangular hyperbola?

x^2 - y^2 = a^2 Signup and view all the answers

What is the angle between the asymptotes of a rectangular hyperbola?

π/2 Signup and view all the answers

What is the length of the latus rectum of a rectangular hyperbola?

2a Signup and view all the answers

If the asymptotes of a hyperbola $x^2 y^2 = 1$ intersect at a point $(h, k)$, what is the value of $h^2 + k^2$?

1 Signup and view all the answers

What is the equation of the conjugate hyperbola of $x^2 y^2 = 1$?

y^2 x^2 = 1 Signup and view all the answers

What is the equation of the hyperbola with asymptotes $y = ±x/2$?

x^2 - 4y^2 = 1 Signup and view all the answers

What is the length of the transverse axis of a hyperbola $x^2 y^2 = 1$?

2 Signup and view all the answers

What is the equation of the tangent to the hyperbola $x^2 y^2 = 1$ at the point $(1, 1)$?

x + y = 2 Signup and view all the answers

If two diameters of a hyperbola are conjugate, what is the product of their slopes?

-1 Signup and view all the answers

What is the equation of the diameter of a hyperbola passing through point Q(h, k)?

y = 2h Signup and view all the answers

If CP is a diameter of a hyperbola x²/a² - y²/b² = 1, where P is (asecφ, btanφ), what are the coordinates of D, where CD is the conjugate diameter of CP?

(atanφ, bsecφ) Signup and view all the answers

What is the condition for the lines AX² + 2HXY + BY² = 0 to be conjugate diameters of a hyperbola?

A = b²/B Signup and view all the answers

What is the relation between the semi-conjugate axis and the eccentricity of a hyperbola, if the equation of the hyperbola is x²/a² - y²/b² = 1?

b = ae Signup and view all the answers

What is the equation of the chord joining points t1 and t2 on the hyperbola xy = c^2?

x + y = c(t1 + t2) Signup and view all the answers

Hyperbola

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Questions and Answers

What is the length of the conjugate axis of a hyperbola?

What is the equation of the transverse axis of a hyperbola?

What is the relation between the semi-conjugate axis and the eccentricity of a hyperbola?

What is the length of the latus rectum of a hyperbola?

What is the equation of a directrix of a hyperbola?

The product of the slopes of CP, CQ, CR and CS is equal to?

If a circle cuts a rectangular hyperbola in A, B, C and D, and the parameters of these four points be t1, t2, t3 and t4 respectively, then what is the value of t1t2t3t4?

What is the condition for a point to divide a line segment in the ratio 1:2?

What is the relationship between the coordinates of P, Q, R and S, where t1, t2, t3 and t4 are the parameters of the points P, Q, R and S respectively?

What is the relationship between H and D, where H is the orthocentre of ΔABC and D is a point on the rectangular hyperbola?

What is the condition for a pair of straight lines?

What is the eccentricity of a rectangular hyperbola?

What is the general equation of a rectangular hyperbola?

What is the angle between the asymptotes of a rectangular hyperbola?

What is the length of the latus rectum of a rectangular hyperbola?

If the asymptotes of a hyperbola $x^2 y^2 = 1$ intersect at a point $(h, k)$, what is the value of $h^2 + k^2$?

What is the equation of the conjugate hyperbola of $x^2 y^2 = 1$?

What is the equation of the hyperbola with asymptotes $y = ±x/2$?

What is the length of the transverse axis of a hyperbola $x^2 y^2 = 1$?

What is the equation of the tangent to the hyperbola $x^2 y^2 = 1$ at the point $(1, 1)$?

If two diameters of a hyperbola are conjugate, what is the product of their slopes?

What is the equation of the diameter of a hyperbola passing through point Q(h, k)?

If CP is a diameter of a hyperbola x²/a² - y²/b² = 1, where P is (asecφ, btanφ), what are the coordinates of D, where CD is the conjugate diameter of CP?

What is the condition for the lines AX² + 2HXY + BY² = 0 to be conjugate diameters of a hyperbola?

What is the relation between the semi-conjugate axis and the eccentricity of a hyperbola, if the equation of the hyperbola is x²/a² - y²/b² = 1?

What is the equation of the chord joining points t1 and t2 on the hyperbola xy = c^2?

What is the point of intersection of tangents at 't1' and 't2' on the hyperbola xy = c^2?

What is the equation of the tangent at (x1, y1) to the hyperbola xy = c^2?

What is the equation of the normal at (x1, y1) to the hyperbola xy = c^2?

What is the coordinate of the foci of the rectangular hyperbola xy = c^2?

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