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If the points {({1},{1})}:{({0},{{}^{{2}}})}; and {({{{e}}}{c}

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If the points $(1, 1) : (0, sec^{2} θ);$ and $(cos e c^{2} θ, 0)$ are collinear, then find the value of $θ$

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If the points

(1, 1) : (0, sec^{2} θ);

and

(cos e c^{2} θ, 0)

are collinear, then find the value of

θ

11 mins ago

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11 mins ago

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Practice questions from similar books

Question 1

PARAGRAPH

X

Let

S

be the circle in the

x y

-plane defined by the equation

x^{2} + y^{2} = 4 .

(For Ques. No 15 and 16)Let

E_{1} E_{2}

and

F_{1} F_{2}

be the chords of

S

passing through the point

P_{0} (1, 1)

and parallel to the x-axis and the y-axis, respectively. Let

G_{1} G_{2}

be the chord of

S

passing through

P_{0}

and having slope

- 1

. Let the tangents to

S

E_{1}

and

E_{2}

meet at

E_{3}

, the tangents to

S

F_{1}

and

F_{2}

meet at

F_{3}

, and the tangents to

S

G_{1}

and

G_{2}

meet at

G_{3}

. Then, the points

E_{3}, F_{3}

and

G_{3}

lie on the curve

x + y = 4

(b)

(x - 4)^{2} + (y - 4)^{2} = 16

(c)

(x - 4) (y - 4) = 4

(d)

x y = 4

View solution

Question 2

Prove that the sum of eccentric angles of four concylic points on the ellipse

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

2 n π,

where

n \in Z

View solution

Question 3

the length of intercept made by the line

2 x - y - 42 = 0

on the parabola

y^{2} = 4 x

is equal to (a)

63

(b)

43

(c)

82

(d)

62

View solution

Question 4

A circle S passes through the point (0, 1) and is orthogonal to the circles

(x - 1)^{2} + y^{2} = 16

and

x^{2} + y^{2} = 1

. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)

View solution

Question Text

If the points

(1, 1) : (0, sec^{2} θ);

and

(cos e c^{2} θ, 0)

are collinear, then find the value of

θ

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If the points (1,1):(0,sec2θ); and (cosec2θ,0) are collinear, then find the value of θ

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Practice questions from similar books

If the points $(1, 1) : (0, sec^{2} θ);$ and $(cos e c^{2} θ, 0)$ are collinear, then find the value of $θ$