1
IIT-JEE 1983
Subjective
+2
-0
The end $$A, B$$ of a straight line segment of constant length $$c$$ slide upon the fixed rectangular axes $$OX, OY$$ respectively. If the rectangle $$OAPB$$ be completed, then show that the locus of the foot of the perpendicular drawn from $$P$$ to $$AB$$ is $${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {c^{{2 \over 3}}}$$
2
IIT-JEE 1983
Fill in the Blanks
+2
-0
The point of intersection of the line 4x - 3y - 10 = 0 and the circle $${x^2} + {y^2} - 2x + 4y - 20 = 0$$ are ........................and ...................
3
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
The centre of the circle passing through the point (0, 1) and touching the curve $$\,y = {x^2}$$ at (2, 4) is
A
$$\left( {{{ - 16} \over 5},{{ - 27} \over {10}}} \right)$$
B
$$\left( {{{ - 16} \over 7},{{53} \over {10}}} \right)$$
C
$$\left( {{{ - 16} \over 5},{{53} \over {10}}} \right)$$
D
none of these
4
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
The equation of the circle passing through (1, 1) and the points of intersection of $${x^2} + {y^2} + 13x - 3y = 0$$ and $$2{x^2} + 2{y^2} + 4x - 7y - 25 = 0$$ is
A
$$4{x^2} + 4{y^2} - 30x - 10y - 25 = 0$$
B
$$4{x^2} + 4{y^2} + 30x - 13y - 25 = 0$$
C
$$4{x^2} + 4{y^2} - 17x - 10y + 25 = 0$$
D
none of these
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