IIT-JEE 2006 | Conic Sections Question 75 | Mathematics

IIT-JEE 2006

MCQ (Single Correct Answer)

-1.5

Match the following : $$(3, 0)$$ is the pt. from which three normals are drawn to the parabola $${y^2} = 4x$$ which meet the parabola in the points $$P, Q $$ and $$R$$. Then

Column $${\rm I}$$
(A) Area of $$\Delta PQR$$
(B) Radius of circumcircle of $$\Delta PQR$$
(C) Centroid of $$\Delta PQR$$
(D) Circumcentre of $$\Delta PQR$$

Column $${\rm I}$$$${\rm I}$$
(p) $$2$$
(q) $$5/2$$
(r) $$(5/2, 0)$$
(s) $$(2/3, 0)$$

$$\left( A \right) - \left( p \right),\left( B \right) - \left( q \right),\left( C \right) - \left( s \right),\left( D \right) - \left( r \right)$$

$$\left( A \right) - \left( p \right),\left( B \right) - \left( q \right),\left( C \right) - \left( r \right),\left( D \right) - \left( s \right)$$

$$\left( A \right) - \left( s \right),\left( B \right) - \left( r \right),\left( C \right) - \left( p \right),\left( D \right) - \left( q \right)$$

$$\left( A \right) - \left( r \right),\left( B \right) - \left( s \right),\left( C \right) - \left( q \right),\left( D \right) - \left( p \right)$$

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 Screening

MCQ (Single Correct Answer)

-0.5

Tangent to the curve $$y = {x^2} + 6$$ at a point $$(1, 7)$$ touches the circle $${x^2} + {y^2} + 16x + 12y + c = 0$$ at a point $$Q$$. Then the coordinates of $$Q$$ are

$$(-6, -11)$$

$$(-9, -13)$$

$$(-10, -15)$$

$$(-6, -7)$$

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-0.5

The angle between the tangents drawn from the point $$(1, 4)$$ to the parabola $${y^2} = 4x$$ is

$$\pi /6$$

$$\pi /4$$

$$\pi /3$$

$$\pi /2$$

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