Podcast
Questions and Answers
What is the length of the conjugate axis of a hyperbola?
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?
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?
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?
What is the length of the latus rectum of a hyperbola?
What is the equation of a directrix 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?
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?
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 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 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 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 condition for a pair of straight lines?
What is the eccentricity of a rectangular hyperbola?
What is the eccentricity of a rectangular hyperbola?
What is the general equation 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 angle between the asymptotes of a rectangular hyperbola?
What is the length of the latus rectum 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 $h^2 + k^2$?
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 conjugate hyperbola of $x^2 y^2 = 1$?
What is the equation of the hyperbola with asymptotes $y = ±x/2$?
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 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 $(1, 1)$?
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?
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)?
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?
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 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 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 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 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 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 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?
What is the coordinate of the foci of the rectangular hyperbola xy = c^2?
