Equation of Tangent, Condition for Tangency and the points of Contact - Advance Quiz

Equation of Tangent, Condition for Tangency and the points of Contact - Advance Quiz

Dear Readers,

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

Q1. If the circle (x-h)^2+(y-k)^2=r^2 is a tangent to the curve y=x^2+1 at a point (1, 2), then the possible location of the points (h, k) are given by :

•  hk=5/2
•  h+2k=5
•  h^2-4k^2=5
•  k^2=h^2+1

Solution
h+2k=5

Q2.If the tangent at the point P on the circle x^2+y^2+6x+6y=2 meets the straight line 5x-2y+6=0at a point Q on the y-axis, then the length of PQ is:

•  4:
•  2√5
•  5
•  3√5

Solution
5

Q3.  The tangents to x^2+y^2=a^2 having inclinations αand β intersect at P. If cot α+cot⁡β=0, then the locus of P is :

•  x+y=0
•  x-y=0
•  xy=0
•  None of these

Solution
xy=0

Q4.  If the points A (1, 4) and B are symmetrical about the tangent to the circle x^2+y^2-x+y=0 at the origin then coordinates of B are

•  (1, 2)
•  x^2+y^2+8x+4=0
•  (4, 1)
•  None of these

Solution
(4, 1)

Q5.A line parallel to the line x-3y=2 touches the circle x^2+y^2-4x+2y-5=0 at the point

•  (1, – 4)
•  (1, 2)
•  (3, – 4)
•  (3, 2)

Solution
 (1, 2)

Q6.  The possible values of p for which the line x cos⁡α+y sin⁡α=p is a tangent to the circle x^2+y^2-2qx cos⁡α-2qy sin⁡α=0 is/are

•  0 and q
•  q and 2q
• 0 and 2q
•  q

Solution
0 and 2q

Q7.A circle passes through (0, 0) and (1, 0) and touches to the circle x^2+y^2=9, then the centre of circle is

•  (3/2,1/2)
•  (1/2,3/2)
•  (1/2,1/2)
•  (1/2,±√2)

Solution
(1/2,±√2)