IIT-JEE 2008 Paper 1 Offline | Ellipse Question 25 | Mathematics

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IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

-1

Consider the two curves $${C_1}:{y^2} = 4x,\,{C_2}:{x^2} + {y^2} - 6x + 1 = 0$$. Then,

$${C_1}$$ and $${C_2}$$ touch each other only at one point.

$${C_1}$$ and $${C_2}$$ touch each other exactly at two points

$${C_1}$$ and $${C_2}$$ intersect (but do not touch ) at exactly two points

$${C_1}$$ and $${C_2}$$ neither intersect nor touch each other

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

-0.5

The minimum area of triangle formed by the tangent to the $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ and coordinate axes is

$$ab$$ sq. units

$${{{{a^2} + {b^2}} \over 2}}$$ sq. units

$${{{{\left( {a + b} \right)}^2}} \over 2}$$ sq. units

$${{{a^2} + ab + {b^2}} \over 3}$$ sq. units

IIT-JEE 2005 Mains

MCQ (Single Correct Answer)

-1

Find the equation of the common tangent in the first quadrant to the circle $$x^{2}+y^{2}=16$$ and the ellipse $$\frac{x^{2}}{25}+\frac{y^{2}}{4}=1$$. Also find the length of the intercept of the tangent between the coordinate axes.

$$\frac{14}{\sqrt5}$$

$$\frac{5}{\sqrt3}$$

$$\frac{14}{\sqrt3}$$

$$\frac{15}{\sqrt3}$$

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-0.5

If tangents are drawn to the ellipse $${x^2} + 2{y^2} = 2,$$ then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

$${1 \over {2{x^2}}} + {1 \over {4{y^2}}} = 1$$

$${1 \over {4{x^2}}} + {1 \over {2{y^2}}} = 1$$

$${{{x^2}} \over 2} + {{{y^2}} \over 4} = 1$$

$${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$$

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