Conic Sections quiz

The eccentricity of a circle is:

The focus of the parabola y^2 = 8x is:

For the ellipse x^2/25 + y^2/16 = 1, the length of the major axis is:

The eccentricity of a parabola is:

For a hyperbola, the relation between a, b and c is:

The radius of the circle x^2 + y^2 = 49 is:

The directrix of the parabola x^2 = 12y is:

The length of the latus rectum of y^2 = 4ax is:

The eccentricity of an ellipse satisfies:

The centre of the circle (x - 3)^2 + (y + 4)^2 = 25 is:

Find the equation of the circle with centre (1, 1) and radius sqrt2. (2 marks)

Find the equation of the parabola with focus (6, 0) and directrix x = -6. (2 marks)

Find the equation of the parabola with vertex (0, 0) and focus (0, 2). (2 marks)

Find the foci and eccentricity of the ellipse x^2/4 + y^2/25 = 1. (2 marks)

Find the length of the latus rectum of the hyperbola 9y^2 - 4x^2 = 36. (2 marks)

Find the equation of the circle with centre (0, 0) passing through (3, 4). (2 marks)

Find the equation of the ellipse whose foci are (4, 0) and (-4, 0) and whose major axis has length 10. (2 marks)

Find the vertices and foci of the hyperbola y^2/9 - x^2/27 = 1. (2 marks)

Find the centre and radius of x^2 + y^2 - 4x - 8y - 45 = 0. (2 marks)

What are the degenerate conic sections? (2 marks)

Find the equation of the parabola symmetric about the x-axis, with vertex at the origin, passing through (2, 3). (3 marks)

Find the equation of the ellipse with centre at the origin, major axis on the y-axis, passing through (3, 2) and (1, 6). (3 marks)

Find the equation of the hyperbola with foci (5, 0) and (-5, 0) and eccentricity 5/3. (3 marks)

A circle passes through (0, 0), (4, 0) and (0, 6). Find its equation. (3 marks)

Find the area of the triangle formed by the vertex and the ends of the latus rectum of the parabola x^2 = 12y. (3 marks)

Read the passage and answer the questions. A satellite dish has a parabolic cross-section with its vertex at the origin and axis along the positive x-axis. The receiver is placed at the focus. The dish is 1 m wide and 25 cm deep. (i) Write the general equation of such a parabola. (ii) Find the focal distance a, using a point on the rim. (iii) Why is the receiver placed at the focus? (5 marks)

Read the passage and answer the questions. The Earth moves around the Sun in an elliptical orbit with the Sun at one focus. Consider an ellipse x^2/25 + y^2/16 = 1 as a simple model of an orbit, with lengths in suitable units. (i) Find c. (ii) Find the eccentricity. (iii) Find the greatest and least distances of a point on the ellipse from the focus. (5 marks)

Read the passage and answer the questions. A circular park has its centre at (2, -3) and passes through the point (5, 1). (i) Find its radius. (ii) Write its equation. (iii) Does the point (6, -3) lie inside, on or outside the park? (5 marks)

Read the passage and answer the questions. A cooling tower has a cross-section in the shape of a hyperbola x^2/9 - y^2/16 = 1, with lengths in tens of metres. (i) Find the vertices. (ii) Find the foci. (iii) Find the eccentricity. (5 marks)

Read the passage and answer the questions. An engineer designs an arch in the form of a parabola with its vertex at the top. The arch is 10 m high and 5 m wide at its base. (i) Taking the vertex at the origin and the axis downward, write the equation form. (ii) Find a using a point at the base. (iii) Find the width of the arch at 2 m below the vertex. (5 marks)

Derive the standard equation of a parabola y^2 = 4ax. Find the focus, directrix and latus rectum of y^2 = -8x. (6 marks)

Derive the standard equation of an ellipse and the relation c^2 = a^2 - b^2. Find the equation of the ellipse with foci (0, 3) and (0, -3) and the length of the major axis 10. (6 marks)

Derive the standard equation of a hyperbola and the relation c^2 = a^2 + b^2. Find all the parameters of 16x^2 - 9y^2 = 576. (6 marks)

Find the equation of the circle passing through (2, -2) and (3, 4) whose centre lies on the line x + y = 2. (6 marks)

A rod of length 12 cm moves with its ends always touching the coordinate axes. Find the equation of the locus of a point P on the rod which is 3 cm from the end in contact with the x-axis. (6 marks)