Chapter 5: Two Dimensional Analytical Geometry II - Online Test

Q1. The equation of the circle passing through (1, 5) and (4,1) and touching y -axis is x2 + y2 − 5x − 6 y + 9 + λ (4x + 3y −19) = 0 where λ is equal to
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Q2. The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is
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Q3. The circle x2 + y2 = 4x + 8 y + 5 intersects the line 3x − 4 y = m at two distinct points if
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Q4. The length of the diameter of the circle which touches the x -axis at the point (1,0) and passes through the point (2, 3)
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Q5. The radius of the circle 3x2 + by2 + 4bx − 6by + b2 = 0 is
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Q6. The centre of the circle inscribed in a square formed by the lines x2 − 8x −12 = 0 and  y2 −14 y + 45 = 0 is
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Q7. The equation of the normal to the circle x2 + y2 − 2x − 2 y +1 = 0 which is parallel to the line 2x + 4 y = 3 is
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Q8. If P(x, y) be any point on 16x2 + 25 y2 = 400 with foci F1 (3, 0) and F2 (−3, 0) then PF1 + PF2 is
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Q9. The radius of the circle passing through the point (6, 2) two of whose diameter are x + y = 6 and x + 2 y = 4 is
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Q10. The area of quadrilateral formed with foci of the hyperbolas  is
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