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Pair of Tangents to a Circle - Basic Quiz

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

Q1. A pair of tangents are drawn from the origin to the circle m(m+n). The equation of the pair of tangents is :
•  x^2+y^2+10xy=0
•  x^2+y^2+5xy=0
•  2x^2+2y^2+5xy=0
•  2x^2+2y^2-5xy=0
Solution
2x^2+2y^2+5xy=0

Q2. The equations of the tangents drawn from the origin to the circle x^2+y^2-2rx-2hy+h^2=0 are:
•  x=0,y=0:
•  (h^2-r^2)x-2rhy=0,x=0
•  y=0,x=4
•  (h^2-r^2)x+2rhy=0,x=0
Solution
AAA(h^2-r^2)x-2rhy=0,x=0

Q3.  The equations of the tangents drawn from the point (0, 1) to the circle x^2+y^2-2x+4y=0 are :
•  2x-y+1=0,x+2y-2=0
•  2x-y+1=0,x+2y+2=0
•  2x-y-1=0,x+2y-2=0
•  2x-y-1=0,x+2y+2=0
Solution
2x-y+1=0,x+2y-2=0

Q4. 193. The two tangents to a circle from an external point are always
•  Equal
•  Perpendicular to each other
•  Parallel to each other
•  None of these
Solution
Equal

Q5.The equation of pair of tangents to the circle x^2+y^2-2x+4y+3=0 from (6, – 5), is
•  7x^2+23y^2+30xy+66x+50y-73=0
•  7x^2+23y^2+30xy-66x-50y-73=0
•  7x^2+23y^2-30xy-66x-50y+73=0
•  None of these
Solution
7x^2+23y^2+30xy+66x+50y-73=0

Q6. Tangents drawn from origin to the circle x^2+y^2-2ax-2by+b^2=0 are perpendicular to each other, if
•  a-b=1
•  a+b=1
• r(< a)
•  a^2+b^2=1
Solution
r(< a)

Q7.The equation to the tangents to the circle x^2+y^2=4, which are parallel to x+2y+3=0, are
•  x-2y=2
•  x+2y=±2√3
•  x+2y=±2√5
•  x-2y=±2√5
Solution
x+2y=±2√5

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