1
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the two circles $${(x - 1)^2} + {(y - 3)^2} = {r^2}$$ and $${x^2} + {y^2} - 8x + 2y + 8 = 0$$
What is the distance between the centres of the two circles?
A
5 units
B
6 units
C
8 units
D
10 units
2
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the two circles $${(x - 1)^2} + {(y - 3)^2} = {r^2}$$ and $${x^2} + {y^2} - 8x + 2y + 8 = 0$$
If the circles intersect at two distinct points, then which one of the following is correct?
A
r = 1
B
1 < r < 2
C
r = 2
D
2 < r < 8
3
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider a circle passing through the origin and the points (a, b) and ($$-$$b, $$-$$a).
On which line does the centre of the circle lie?
A
x + y = 0
B
x $$-$$ y = 0
C
x + y = a + b
D
x $$-$$ y = a2 $$-$$ b2
4
NDA 2016 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Consider a circle passing through the origin and the points (a, b) and ($$-$$b, $$-$$a).
What is the sum of the squares of the intercepts cut-off by the circle on the axes?
A
$${\left( {{{{a^2} + {b^2}} \over {{a^2} - {b^2}}}} \right)^2}$$
B
$$2{\left( {{{{a^2} + {b^2}} \over {a - b}}} \right)^2}$$
C
$$4{\left( {{{{a^2} + {b^2}} \over {a - b}}} \right)^2}$$
D
None of these
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