JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

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Application +4 | -1

a, x_1, x_2

are in G.P. with common ratio

r

, and

b, y_1, y_2

are in G.P. with common ratio

s

where

s-r=2

, then the area of the triangle with vertices

(a, b)

\left(x_1, y_1\right)

and

\left(x_2, y_2\right)

View answer and explanation

Correct option: A

\left|a b\left(r^2-1\right)\right|

Option C ((0,0)) is correct because the triangle formed by the lines is a right-angled triangle at the origin, and the orthocenter of a right-angled triangle is the vertex at the right angle.

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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