GUJCET Conic Sections — practice questions
48 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice GUJCET Conic Sections in the app →For the standard form of a **horizontal** ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ with $0 < b < a$, 
From the figure, the vertices of the horizontalFind the eccentricity of the ellipse $\dfrac{x^2}{25} + \dfrac{y^2}{16} = 1$.The foci of the ellipse $\dfrac{x^2}{25} + \dfrac{y^2}{16} = 1$ lie at:For an ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ ($a > b$), the **length of the latus rectum** is:An ellipse has foci at $(\pm 4, 0)$ and passes through the point $(5, 0)$. Find its standard equation.
The figure shows a parabola opening to the *
For the parabola $y^2 = 4ax$ ($a > 0$), the Find the length of the latus rectum of the parabola $y^2 = 8x$.Find the equation of the parabola with vertex at the origin and focus at $(0, -3)$.A parabola has its vertex at the origin, its axis along the positive $x$-axis, and passes through the point $(For the parabola $y^2 = 16x$, find the equation of the directrix.The standard equation of a hyperbola with centre at the origin and foci on the $x$-axis is:For any hyperbola, the eccentricity $e$ satisfies:
Find the foci of the hyperbola $\dfrac{x^2}{What is the eccentricity of the hyperbola $\dfrac{x^2}{9} - \dfrac{y^2}{16} = 1$?
For any point $P$ on a hyperbola with foci $A hyperbola has foci at $(\pm 5, 0)$ and the length of the transverse axis is $6$. Find its equation.$ in(180° - \theta)$ equals:$ in^2\theta + \cos^2\theta$ equals:$ in(A + B) = $sin(0°) equals:cos(90°) equals:sin²θ + cos²θ equals:tan(45°) equals:In which quadrant is sin θ positive and cos θ negative?Equation of circle with center (h, k) and radius r:Standard ellipse x²/a² + y²/b² = 1 (a > b) has eccentricity:Hyperbola x²/a² - y²/b² = 1 has eccentricity:Latus rectum of parabola y² = 4ax:Equation of tangent to parabola y² = 4ax at point (at², 2at):Axis of symmetry of parabola x² = 4ay (a > 0):Asymptotes of hyperbola x²/a² - y²/b² = 1:Equation of normal to parabola y² = 4ax at (at², 2at):Conjugate hyperbola of x²/a² - y²/b² = 1:Equation of circle passing through origin, (a, 0), (0, b):Tangent to circle x² + y² = r² at point (x₁, y₁):Find focus and directrix of parabola y² = -8x:Eccentricity of hyperbola 9x² - 16y² = 144:Length of latus rectum of ellipse x²/25 + y²/9 = 1:Common tangent to circle x² + y² = 5 and parabola y² = 8x:Eccentricity of ellipse: x² + 4y² = 4:For parabola y² = 4ax, point (at², 2at) gives parametric form. If t = 2 and a = 3:Sum of distances from any point on ellipse 9x² + 16y² = 144 to its foci:Difference of focal distances from any point on hyperbola x²/16 - y²/9 = 1:For hyperbola x²/25 - y²/144 = 1, find length of conjugate axis:Auxiliary circle of ellipse x²/a² + y²/b² = 1:Relation between eccentricities of conjugate hyperbolas: