Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 22

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The line $y = a - x$ touches the parabola $y = x - x^{2}$ and $f (x) = \sin^{2} x + \sin^{2} (x + \frac{π}{3}) + \cos x \cdot \cos (x + \frac{π}{3})$ then

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Important Questions on Conic Section

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 23

The coordinates of the point on the parabola

y^{2} = 8 x

which is at a minimum distance from the circle

x^{2} + {(y + 6)}^{2} = 1

are

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 24

If a circle intersects the parabola

y^{2} = 4 a x,

at points

A (a t_{1}^{2}, 2 a t_{1}), B (a t_{2}^{2}, 2 a t_{2}), C (a t_{3}^{2}, 2 a t_{3}), D (a t_{4}^{2}, 2 a t_{4})

then

t_{1} + t_{2} + t_{3} + t_{4} =

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 25

If the line

y - \sqrt{3} x + 3 = 0

cuts the parabola

y^{2} = x + 2

at

A

and

B

. If

P \equiv (\sqrt{3}, 0)

then

P A \cdot P B

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 26

A ray of light moving parallel to

x

-axis gets reflected from a parabolic mirror whose equation is

4 (x + y) - y^{2} = 0 .

After reflection the ray pass through the point

(a, b)

. Then the value of

a + b

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 27

If the parabola

y = (a - b) x^{2} + (b - c) x + (c - a)

touches the

x

-axis then the line

a x + b y + c = 0

always passes through a fixed point is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 28

The vertex of a parabola

y^{2} = 8 x

is at the centre of a circle and parabola cuts the circle at ends of its latus rectum. Then, equation of the circle is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 29

The mirror image of the focus to the parabola

4 (x + y) = y^{2}

w.r.t. the directrix is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 30

Let

m_{1}, m_{2}

are slopes of two tangents that are drawn from

(2, 3)

to the parabola

y^{2} = 4 x

and

α

is the harmonic mean of

m_{1} & m_{2}

. If

β

is the value of

(1 + \tan 23 °) (1 + \tan 22 °)

, then

\frac{3}{2} α + β

is