Practice Test

Q1) A normal to any circle always lies along its Show Answer

Q2) If lines 12x + 5y + 16 = 0 and 12x + 5y - 10 = 0 both touch the same circle, then radius of this circle is Show Answer

Q3) If equation of common tangent at (1, -1) to two circles, each of radius 13, is 12x + 5y - 7 = 0, then centres of circles are Show Answer

Q4) Line 3x + y = 0 touches a circle centered at (2,-1). Then, other tangent to this circle from the origin is Show Answer

Q5) If two circles of same radius r and centres at (2, 3) and (5, 6) cut each other orthogonally, then r = Show Answer

Q6) Radius of the larger circle in the first quadrant which touches the line 4x + 3y - 12 = 0, and the co-ordinate axes, is Show Answer

Q7) Centre of the circle lies on the line x + 2y = 3 as well as on the bisector of the angle in the first quadrant. If this circle touches the line 4x + 8y = 7, then its area is Show Answer

Q8) A circle touches both the axes, and the line 4x + 3y = 6 in the first quadrant. If it lies entirely below the line, then its equation is Show Answer

Q9) The equation of the circle having x - y - 2 = 0 and x - y + 2 = 0 as two tangents, and x - y = 0 as a diameter, is Show Answer

Q10) If two circles cut each other orthogonally, then Show Answer

Q11) Tangents at the ends of a focal chord of a parabola meet each other Show Answer

Q12) The only real normal to a parabola, passing through its focus, is its Show Answer

Q13) Point of intersection of two perpendicular tangents to a parabola lies on the Show Answer

Q14) If the product of lengths of perpendiculars drawn from the foci of a hyperbola to its tangent 2x - y + 4 = 0 is 9, then the equation of this hyperbola is Show Answer

Q15) Equation of circle centred at (2, -3), and passing through (-1, 2), is Show Answer

Q16) Equation of circle centred at (5, -2), and touching X – axis, is Show Answer

Q17) Equation of circle centred at (-4, 3), and tangent to Y – axis, is Show Answer

Q18) Equation of circle centred on X-axis, and passing through (6, 4) and (8, -4), is Show Answer

Q19) Equation of circle passing through (-2, 0), (4, 0), and having radius 5, is Show Answer

Q20) Equation of circle passing through (0, 0), (3, 0) and (0, -2) is Show Answer

Q21) Equation of circle through the origin, having intercepts (6) and (-4) on X- and Y – axes respectively, is Show Answer

Q22) Equation of circle of radius 5, centred on X-axis and touching Y-axis, is Show Answer

Q23) Equation of circle of radius 5, centred on Y-axis and touching X-axis, is Show Answer

Q24) Equation of circle of radius 5, centred on X-axis and passing through origin is Show Answer

Q25) Equation of circle of radius 5, centred on Y-axis and passing through origin, is Show Answer

Q26) Equation of circle of radius 5, touching both co-ordinate axes, and passing through (1, 2) is Show Answer

Q27) Equation of circle having radius 5, and touching X-axis at (-1, 0), is Show Answer

Q28) Equation of circle through origin, having radius 5 and abscissa of centre (-3), is Show Answer

Q29) Centre of circle, passing through (0, 0), (a, 0) and (0, b) is Show Answer

Q30) If the circle described on the join of (2, 3) and (3, a) as a diameter passes through the origin, then : a = Show Answer

Q31) Equation of the circle with centre on X-axis, radius 5, and passing through (2, 3) is Show Answer

Q32) Equation of circumcircle of square OACB of side a, where OA and OB are along coordinate axes, is Show Answer

Q33) Equation of circle which touches both axes at a distance of 4 units from origin is Show Answer

Q34) Length of the diameter of the circle which touches the X-axis at the point (1, 0), and passes through the point (2, 3) is Show Answer