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Length of Tangent - Advance Quiz

Mathematics is an important subject in SSC,DSSB & Other Exams. .

Q1. The coordinates of the point from where the tangents are drawn to the circles x^2+y^2=1, x^2+y^2+8x+15=0 and √3 x-y=2 are of same length, are :
•  (2,5/2)
•  (-2,-5/2)
•  (-2,5/2)
•  (2,-5/2)
Solution
(-2,-5/2)

Q2.Length of the tangent drawn from any point on the circle x^2+y^2+2gx+2fy+c_1=0 to the circle x^2+y^2+2gx+2fy+c=0 is:
•  √(c_1-c):
•  √(c-c_1 )
•  √(c_1+c)
•  None of these
Solution
√(c-c_1 )

Q3.   If P is a point such that the ratio of the squares of the lengths of the tangents from P to the circles x^2+y^2+2x-4y-20=0 and x^2+y^2-4x+2y-44=0 is 2 : 3, then the locus of P is a circle with centre :
•  (7, – 8)
•  (-7, 8)
•  (7, 8)
•  (-7,-8)
Solution
(-7, 8)

Q4. The lengths of the tangents from any point on the circle 15x^2+15y^2-48x+64y=0 to the two circles 5x^2+5y^2-24x+32y+75=0,5x^2+5y^2-48x+64y+300=0 are in the ratio
•  1 : 2
•  2 : 3
•  3 : 4
•  None of these
Solution
1 : 2

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