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Conic Section Practice Test Online Mcqs

Test Name Conic Section Practice Test
Subject Math
Test Type Mcqs
Total Question 12
Total Marks 24
Total Time 12
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In mathematics, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it was sometimes called a fourth type of conic section. The conic sections of the Euclidean plane have various distinguishing properties. Many of these have been used as the basis for a definition of the conic sections. One such property defines a non-circular conic to be the set of those points whose distances to some particular point, called a focus, and some particular line, called a directrix, are in a fixed ratio, called the eccentricity. The type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2; that is, as the set of points whose coordinates satisfy a quadratic equation in two variables. This equation may be written in matrix form, and some geometric properties can be studied as algebraic conditions.

Conic Section Practice Test Online Mcqs

Math

1. For what value of k, the line x + y = 1 touches the parabola y2 = kx.

Question 1 of 12

2. Consider the set of hyperbola xy = k, k ∈ R. Let e1 and ebe the eccentricties when k = 16 and k = 16 and k = 25 respectively then the value of e21 - e22 equals

Question 2 of 12

3. Let E be the ellipse x2/9 + y2/4 = 1 and C be the circle centred at (0, 0) with radius 3. Let P and Q be the points (1, 2) and (2, 1) respectively then

Question 3 of 12

4. The locus of the point of intersection of the lines √3x - y - 4√3k = 0 and √3kx - ky- 4√3 = 0 represent a hyperbola then eccentricity equals:

Question 4 of 12

5. Consider an ellipse and concentric circle. The circle passes through the foci of the ellipse and intersects the ellipse in four distinct points. The length of major axis of the ellipse is 15 units. If S1 and S2 are the foci of the ellipse, P be one of point of intersection of ellipse and circle and area of triangle PS1S2 is 26 sq. units, then eccentricity  of the ellipse is equal to

Question 5 of 12

6. If x + y = k is normal to the parabola y2 = 12x then k equals

Question 6 of 12

7. The curved described parametrically by x = t2 + t + 1 and y = t2 - t + 1 represent

Question 7 of 12

8. The second degree equation x2 + 4y2 + 2x + 16y + 13 = 0 represent itself as:

Question 8 of 12

9. If the line 2x - 1 = 0 is the directrix of the parabola y2 - kx + 6 = 0 then one of the values of k is

Question 9 of 12

10. The equation of the chord of y2 = 8x which is bisected at (2, -3) is:

Question 10 of 12

11. Consider a point P on the ellipse x2/a2 + y2/b2 = 1 and a corresponding point Q on its auxiliary circle. If R be the foot of perpendicular drawn from focus S1 to the tangent drawn to the auxiliary circle at Q then triangle S1PR is necessarily

Question 11 of 12

12. The length of the latus-rectum of the parabola ay2 + by = x - c is:

Question 12 of 12


 

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