1
JEE Advanced 2017 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
By appropriately matching the information given in the three columns of the following table.
Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.
Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.
Column - 1 | Column - 2 | Column - 3 | |
---|---|---|---|
(i) | $${x^2} + {y^2} = a$$ | $$my = {m^2}x + a$$ | $$\left( {{a \over {{m^2}}},\,{{2a} \over m}} \right)$$ |
(ii) | $${x^2}{a^2}{y^2} = {a^2}]$$ | $$y = mx + a\sqrt {{m^2} + 1} $$ | $$\left( {{{ - ma} \over {\sqrt {{m^2} + 1} }},\,{a \over {\sqrt {{m^2} + 1} }}} \right)$$ |
(iii) | $${y^2} = 4ax$$ | $$y = mx + \sqrt {{a^2}{m^2} - 1} $$ | $$\left( {{{ - {a^2}m} \over {\sqrt {{a^2}{m^2} + 1} }},\,{1 \over {\sqrt {{a^2}{m^2} + 1} }}} \right)$$ |
(iv) | $${x^2} - {a^2}{y^2} = {a^2}$$ | $$y = mx + \sqrt {{a^2}{m^2} + 1} $$ | $$\left( {{{ - {a^2}m} \over {\sqrt {{a^2}{m^2} - 1} }},\,{{ - 1} \over {\sqrt {{a^2}{m^2} - 1} }}} \right)$$ |
For $$a = \sqrt 2 $$, if a tangent is drawn to a suitable conic (Column 1) at the point of contact ($$-$$1, 1), then which of the following options is the only CORRECT combination for obtaining its equation?
2
JEE Advanced 2017 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
By appropriately matching the information given in the three columns of the following table.
Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.
Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.
Column - 1 | Column - 2 | Column - 3 | |
---|---|---|---|
(i) | $${x^2} + {y^2} = a$$ | $$my = {m^2}x + a$$ | $$\left( {{a \over {{m^2}}},\,{{2a} \over m}} \right)$$ |
(ii) | $${x^2}{a^2}{y^2} = {a^2}]$$ | $$y = mx + a\sqrt {{m^2} + 1} $$ | $$\left( {{{ - ma} \over {\sqrt {{m^2} + 1} }},\,{a \over {\sqrt {{m^2} + 1} }}} \right)$$ |
(iii) | $${y^2} = 4ax$$ | $$y = mx + \sqrt {{a^2}{m^2} - 1} $$ | $$\left( {{{ - {a^2}m} \over {\sqrt {{a^2}{m^2} + 1} }},\,{1 \over {\sqrt {{a^2}{m^2} + 1} }}} \right)$$ |
(iv) | $${x^2} - {a^2}{y^2} = {a^2}$$ | $$y = mx + \sqrt {{a^2}{m^2} + 1} $$ | $$\left( {{{ - {a^2}m} \over {\sqrt {{a^2}{m^2} - 1} }},\,{{ - 1} \over {\sqrt {{a^2}{m^2} - 1} }}} \right)$$ |
The tangent to a suitable conic (Column 1) at $$\left( {\sqrt 3 ,\,{1 \over 2}} \right)$$ is found to be $$\sqrt 3 x + 2y = 4$$, then which of the following options is the only CORRECT combination?
3
JEE Advanced 2017 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
By appropriately matching the information given in the three columns of the following table.
Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.
Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.
Column - 1 | Column - 2 | Column - 3 | |
---|---|---|---|
(i) | $${x^2} + {y^2} = a$$ | $$my = {m^2}x + a$$ | $$\left( {{a \over {{m^2}}},\,{{2a} \over m}} \right)$$ |
(ii) | $${x^2}{a^2}{y^2} = {a^2}]$$ | $$y = mx + a\sqrt {{m^2} + 1} $$ | $$\left( {{{ - ma} \over {\sqrt {{m^2} + 1} }},\,{a \over {\sqrt {{m^2} + 1} }}} \right)$$ |
(iii) | $${y^2} = 4ax$$ | $$y = mx + \sqrt {{a^2}{m^2} - 1} $$ | $$\left( {{{ - {a^2}m} \over {\sqrt {{a^2}{m^2} + 1} }},\,{1 \over {\sqrt {{a^2}{m^2} + 1} }}} \right)$$ |
(iv) | $${x^2} - {a^2}{y^2} = {a^2}$$ | $$y = mx + \sqrt {{a^2}{m^2} + 1} $$ | $$\left( {{{ - {a^2}m} \over {\sqrt {{a^2}{m^2} - 1} }},\,{{ - 1} \over {\sqrt {{a^2}{m^2} - 1} }}} \right)$$ |
If a tangent to a suitable conic (Column 1) is found to be y = x + 8 and its point of contact is (8, 16), then which of the following options is the only CORRECT combination?
4
JEE Advanced 2016 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-0
Let $${F_1}\left( {{x_1},0} \right)$$ and $${F_2}\left( {{x_2},0} \right)$$ for $${{x_1} < 0}$$ and $${{x_2} > 0}$$, be the foci of the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 8} = 1$$. Suppose a parabola having vertex at the origin and focus at $${F_2}$$ intersects the ellipse at point $$M$$ in the first quadrant and at point $$N$$ in the fourth quadrant.
If the tangents to the ellipse at $$M$$ and $$N$$ meet at $$R$$ and the normal to the parabola at $$M$$ meets the $$x$$-axis at $$Q$$, then the ratio of area of the triangle $$MQR$$ to area of the quadrilateral $$M{F_1}N{F_2}$$is
Questions Asked from Conic Sections (MCQ (Single Correct Answer))
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