Home
Class 12
MATHS
If the pair of lines ax^(2)+2hxy+by^(2)+...

If the pair of lines `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0` intersect on the y-axis , then prove that `2fgh=bg^(2)+ch^(2)`.

A

`f^2=bc`

B

abc=2fgh

C

`bg^2 ne ch^2`

D

`2 fgh = bg^2+ch^2`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|9 Videos
  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|2 Videos
  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|10 Videos
  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|29 Videos
  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|36 Videos

Similar Questions

Explore conceptually related problems

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2.

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

The circle x^(2) + y^(2) + 2g x + 2fy + c = 0 does not intersect the y-axis if

the equation ax^(2)+ 2hxy + by^(2) + 2gx + 2 fy + c=0 represents an ellipse , if

If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 respresent the pair of parallel straight lines , then prove that h^(2)=abandabc+2fgh-af^(2)-bg^(2)-ch^(2)=0 .

If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents a pair of parallel lines, then

The equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 repersents a hyperbola if

If the slopes of the lines given by ax^(2)+2hxy+by^(2)=0 are in the ratio 3:1 , then h^(2)=

If ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents parallel straight lines, then