Home
Class 12
MATHS
Prove that the equation (a+2h+b)x^2-2(a...

Prove that the equation `(a+2h+b)x^2-2(a-b)xy+(a-2h+b)y^2=0` represents a pair of lines each inclined at an angle of `45^@` to one or other of the lines given by , `ax^2+2hxy+by^2=0`

Text Solution

Verified by Experts

The correct Answer is:
`therefore (a+2h+b)x^2-2(a-b)xy+(a-2h+b)y^2=0`
Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|9 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|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

Prove that the equation m (x^3-3xy^2)+y^3-3x^2y=0 represents three straight lines equally inclined to each other.

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

The equation kx^2+4xy+5y^2=0 represents two lines inclined at an angle pi if k is

The equation 3ax^2+9xy+(a^2-2)y^2=0 represents two perpendicular straight lines for

if h^2=ab , then the lines represented by ax^2+2hxy+by^2=0 are

The value of h for which 3x^2-2hxy + 4y^2 = 0 represents a pair of coincident lines are

The equation a^2x^2+2h(a+b)x y+b^2y^2=0 and a x^2+2h x y+b y^2=0 represent

The equation a^2x^2+2h(a+b)x y+b^2y^2=0 and a x^2+2h x y+b y^2=0 represent

The set of value of h for which the equation 4x^(2)+hxy-3y^(2)=0 represents a pair of real and distinct lines is

The equation 3x^2+2hxy+3y^2=0 represents a pair of straight lines passing through the origin . The two lines are