JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

1 Easy

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Application +4 | -1

The product of perpendiculars let fall from the point

\left(x_1, y_1\right)

upon the lines represented by

a x^2+2 h x y+b y^2

, is

View answer and explanation

Correct option: A

\frac{\left|a x_1^2+2 h x_1 y_1+b y_1^2\right|}{\sqrt{(a-b)^2+4 h^2}}

The correct answer is A (

\frac{{\left|a x_1^2+2 h x_1 y_1+b y_1^2\right|}}{{\sqrt{{(a-b)^2+4 h^2}}}}

) because it represents the product of perpendicular distances from a point to the lines represented by the given equation, derived using the sum and product of slopes.

More Questions from PAIR OF STRAIGHT LINES

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a x^2+2 h x y+b y^2+2 g x+2 f y+c=0

represents parallel straight lines, then Image of the point

(-1,3)

with respect to the line

y=2 x

is If the pair of lines represented by

a x^2+2 h x y+b y^2+2 g x+2 f y+c=0

intersect on

y

-axis, then If the sum of the slopes of the lines given by

4 x^2+2 \lambda x y-7 y^2=0

is equal to the product of the slopes, then

\lambda

is equal to The equation

3 x^2+2 h x y+3 y^2=0

represents a pair of straight lines passing through the origin. The two lines are The value of

h

for which

3 x^2-3 h x y+4 y^2=0

represents a pair of coincident lines are