Test on Conic Section
Group 01
Section A – 2 Marks each
- The equation of a parabola is \(y^2 = 4ax\). What will be its line of symmetry? Find its latus rectum.
- When the axis of symmetry is along the x-axis the parabola opens to the ______ if the coefficient of \(x\) is _________ . Draw its graph.
Section B – 3 Marks each
- Define ellipse. Write their general equations.
- Find the equation of the ellipse, whose length of the major axis is 24 and foci are \((0, ± 6)\). Find its latus rectum.
Section C – 5 Marks each
- Find the coordinates of the foci, the vertices, the length of transverse axis, the conjugate axis, the eccentricity and the latus rectum of the hyperbola \(25 x^2 -9y^2 = 225\)
Group 02
Section A – 2 Marks each
- The equation of an ellipse is \(\frac{x^2}{a^2} +\frac{y^2}{b^2} = 1\). What will be its lines of symmetry? Find its latus rectum.
- The foci of ellipse lie always on its ________ axis. If the coefficient of \(y^2\) has larger denominator than that of \(x^2\) then major axis will be ________.
Section B – 3 Marks each
- Define hyperbola. Write their general equations.
- Find the equation of the hyperbola, whose foci are \((0, ± 5)\) and vertices are \((0, ± 7)\). Find its latus rectum.
Section B – 5 Marks each
- The equation of a parabola is \(x^2 = 28 y\). Find the coordinates of its focus, and vertex. Also write the equations of its directrix and its axis. What is its latus rectum?
Write the general equation of circle with center \((a,b)\) and radius \(r\).
Group 03
Section A – 2 Marks each
- The equation of an hyperbola is \(\frac{x^2}{a^2} – \frac{y^2}{b^2} = 1\). What will be its lines of symmetry? Find its latus rectum.
- The foci of hyperbola lie always on its ________ axis. If the coefficient of \(x^2\) is negative then its conjugate axis will be along ________.
Section B – 3 Marks each
- Find the equation of the parabola which is symmetric about the y-axis, and passes through the point (-3,4). Also find its latus rectum.
- Define parabola. Write their general equations.
Section C – 5 Marks each
- Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the latus rectum of the ellipse \(9 x^2 + 25y^2 = 225\)