Hyperbola
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Questions and Answers

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?

    <p>2a(e^2 - 1)</p> Signup and view all the answers

    What is the equation of a directrix of a hyperbola?

    <p>x = -ae</p> Signup and view all the answers

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

    <p>-1</p> 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?

    <p>-1</p> Signup and view all the answers

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

    <p>16x^2 + 10xy + y^2 = 2</p> 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>P(ct1, t1), Q(ct2, t2), R(ct3, t3), S(ct4, t4)</p> 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?

    <p>H and D are the extremities of a diagonal of the rectangular hyperbola</p> Signup and view all the answers

    What is the condition for a pair of straight lines?

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

    What is the eccentricity of a rectangular hyperbola?

    <p>2</p> Signup and view all the answers

    What is the general equation of a rectangular hyperbola?

    <p>x^2 - y^2 = a^2</p> Signup and view all the answers

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

    <p>π/2</p> Signup and view all the answers

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

    <p>2a</p> 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 $h^2 + k^2$?

    <p>1</p> Signup and view all the answers

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

    <p>y^2 x^2 = 1</p> Signup and view all the answers

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

    <p>x^2 - 4y^2 = 1</p> Signup and view all the answers

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

    <p>2</p> Signup and view all the answers

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

    <p>x + y = 2</p> Signup and view all the answers

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

    <p>-1</p> Signup and view all the answers

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

    <p>y = 2h</p> 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?

    <p>(atanφ, bsecφ)</p> Signup and view all the answers

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

    <p>A = b²/B</p> 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?

    <p>b = ae</p> Signup and view all the answers

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

    <p>x + y = c(t1 + t2)</p> Signup and view all the answers

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

    <p>(2ct1t2 / (t1 + t2), 2ct1t2 / (t1 + t2))</p> Signup and view all the answers

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

    <p>xy1 + yx1 = 2c^2</p> Signup and view all the answers

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

    <p>xx1 - yy1 = x1^2 - y1^2</p> Signup and view all the answers

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

    <p>(±c, ±c)</p> Signup and view all the answers

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