Practice Test

Q1) If (0, 4) and (0, 2) are respectively the vertex and focus of the parabola, then its equation is Show Answer

Q2) If (2, 0) is the vertex and y-axis the directrix of a parabola, then its focus is Show Answer

Q3) Two ends of the latus rectum of a parabola are the points (3, 6) and (-5, 6). The focus is Show Answer

Q4) Two ends of latus rectum of a parabola are the points (3, 6) and (-5, 6), the focus is Show Answer

Q5) A man running round a race course notes that the sum of the distances of two flag-posts from him is always 10 meters and the distance between the flag-posts is 8 meters. The area of the path he encloses in square meters is Show Answer

Q6) The latus rectum of an ellipse is equal to half of its minor axis. Then, its eccentricity is Show Answer

Q7) If two unequal parabolas have the same focus and axis in opposite directions, then the angle between them at their common tangents is Show Answer

Q8) The area of the loop between the curve y = a sin x and x-axis is Show Answer

Q9) The two ends of latusrectum of a parabola are the points (3, 6) and (-5, 6), then the focus is Show Answer

Q10) If (0, 4) and (0, 2) are respectively, the vertex and focus of a parabola, then its equation is Show Answer

Q11) The length of the latusrectum of the parabola, whose focus is (3, 3) and directrix is 3x - 4y - 2 = 0, is Show Answer

Q12) The eccentricity of ellipse, if length of major axis is three times the length of minor axis Show Answer

Q13) The curve with parametric equations x = 1 + 4 cos t, y = 2 + 3 sin t is Show Answer

Q14) In an ellipse, the distance between its foci is 6 and its minor axis is 8. Then, its eccentricity is Show Answer

Q15) A man running round a race course notes that the sum of the distances of two flag posts from him is always 10 m and the distance between the flag posts is 8 m. The area of the path he encloses in square meters is Show Answer

Q16) S and S' are the foci of an ellipse and B is an end of the minor axis. If SS' B is an equilateral triangle, then eccentricity of the ellipse is Show Answer

Q17) In an ellipse, the distance between the foci is 8 and the distance between the directrices is 25. The length of major axis is Show Answer

Q18) The curve represented by x = 3 (cot t + sin t), y = 4 (cos t - sin t) is Show Answer

Q19) The eccentricity of the hyperbola, whose latusrectum is 8 and conjugate axis is equal to half the distance between the foci is Show Answer

Q20) the equation of hyperbola is Show Answer

Q21) the focus of hyperbola is Show Answer

Q22) Equation of a tangent common to both the parabola P and the ellipse E is Show Answer

Q23) Equation of the normal at the point of contact of the common tangent, which makes an acute angle with the positive direction of X-axis, to the parabola P is Show Answer

Q24) Point of contact of a common tangent to P and E on the ellipse is Show Answer

Q25) A point P moves such that its distances from (1, 2) and (-2, 3) are equal. Then, the locus of P is Show Answer

Q26) The difference of focal distances of any point on a hyperbola is equal to Show Answer

Q27) The eccentricity e of an ellipse satisfies the condition Show Answer

Q28) What is the locus of points, the difference of whose distances from tow points being constant? Show Answer

Q29) The eccentricity of ellipse, if the length of latusrectum is half of minor axis, is Show Answer

Q30) If (4, 0) and (-4, 0) are the foci of an ellipse and the semi-minor axis is 3, then the ellipse passes through which one of the following points? Show Answer

Q31) What is the sum of focal radii of any point on an ellipse equal to? Show Answer