Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 13

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$A B C D$ is a square away from origin of side length $' a'$ . Its side $A B$ slides between $x$ and $y$ -axes in first quadrant with $A$ on $x$ -axis and $B$ on $y$ -axis. The locus of the foot of perpendicular dropped from the point $E$ on the diagonal $A C$ (where $E$ is the midpoint of the side $A D$ ) is

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Important Questions on Point and Straight Line

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 14

The locus of circumcentre of the triangle formed by vertices

A ((- p q - p - q), - (1 + p) (1 + q)), B (p q + p - q, (1 + p) (1 + q)), C (p q + q - p, (1 + p) (1 + q))

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 15

Let two sides of rectangle of area

20

sq. units are along lines

x - y = 0

and

x + y = 2,

then the locus of point of intersection of diagonals is:

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 16

Area of the triangle formed by the line

x + y = 3

and the angle bisectors of the pairs of straight lines

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

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 17

Equation of the line pair through the origin and perpendicular to the line pair

x y - 3 y^{2} + y - 2 x + 10 = 0

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 18

Find the equation of the two straight lines which together with those given by the equation

6 x^{2} - x y - y^{2} + x + 12 y - 35 = 0

will make a parallelogram whose diagonals intersect in the origin.

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 19

The curve passing through the points of intersection of

S_{1} \equiv \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} - 1 = 0

and

S_{2} \equiv x^{2} + y^{2} + 2 g x + 2 f y + c = 0

represents a pair of straight lines which are

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 20

If the points

(\frac{a^{3}}{a - 1}, \frac{a^{2} - 3}{a - 1}), (\frac{b^{3}}{b - 1}, \frac{b^{2} - 3}{b - 1})

and

(\frac{c^{3}}{c - 1}, \frac{c^{2} - 3}{c - 1})

are collinear for three distinct values

a, b, c

and

a \neq 1, b \neq 1

and

c \neq 1,

then find the value of

a b c - (a b + b c + a c) + 3 (a + b + c) .

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 21

Find the number of integral values of

λ

if

(λ, λ + 1)

is an interior point of

Δ A B C,

where

A \equiv (0, 3) B \equiv (- 2, 0)

and

C = (6, 1) .