1
IIT-JEE 2005
Subjective
+2
-0
Circles with radii 3, 4 and 5 touch each other externally. It P is the point of intersection of tangents to these circles at their points of contact, find the distance of P from the points of contact.
2
IIT-JEE 2005
Subjective
+4
-0
Tangents are drawn from any point on the hyperbola $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$ to the circle $${x^2} + {y^2} = 9$$.Find the locus of mid-point of the chord of contact.
3
IIT-JEE 2005
Subjective
+4
-0
Find the equation of the common tangent in $${1^{st}}$$ quadrant to the circle $${x^2} + {y^2} = 16$$ and the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over 4} = 1$$. Also find the length of the intercept of the tangent between the coordinate axes.
4
IIT-JEE 2005
MCQ (Single Correct Answer)
+2
-0.5
In an equilateral triangle, $$3$$ coins of radii $$1$$ unit each are kept so that they touch each other and also the sides of the triangle. Area of the triangle is IIT-JEE 2005 Mathematics - Properties of Triangle Question 9 English
A
$$4 + 2\sqrt 3 $$
B
$$6 + 4\sqrt 3 $$
C
$$12 + {{7\sqrt 3 } \over 4}$$
D
$$3 + {{7\sqrt 3 } \over 4}$$
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