Home
Class 12
MATHS
Consider a pair of perpendicular straigh...

Consider a pair of perpendicular straight lines `ax^(2)+3xy-2y^(2)-5x+5y+c=0`.
The value of a is

A

1

B

3

C

2

D

-2

Text Solution

Verified by Experts

The correct Answer is:
3
As the lines are perpendicular, Coefficient of `x^(2)+` Coefficient of `y^(2)=0`
`:.a-2=0`
or `a=2`
Also , `abc+2fgh-af^(2)-bg^(2)-ch^(2)=0`
`:. c=-3`
Hence , the given pair of lines is
`2x^(2)+3xy-2y^(2)-5x+5y-3=0`
Factorizing , we get lines
`x+2y-3=0and 2x-y+1=0`

The point of intersection of the lines is C `(1//5,7//5)`.
The points of intersection of the lines with the x- axis are A(3,0) and B `(-1//2,0)`.
The orthocenter of triangle is C `(1//5,7//5)` and the circumcenter is the midpoint of AB which is M `(5//4,0)`. Therefore,
CM`sqrt(((5)/(4)-(1)/(5))^(2)+(49)/(25))=(7)/(4)`
Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Multiple)|9 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

  • PARABOLA

    CENGAGE|Exercise Question Bank|9 Videos

Similar Questions

Explore conceptually related problems

Consider a pair of perpendicular straight lines ax^(2)+3xy-2y^(2)-5x+5y+c=0 . The value of c is

Consider the equation of a pair of straight lines as lambdax^(2)-10xy+12y^(2)+5x-16y-3=0 . The angles between the lines is theta . Then the value of tan theta is

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 (a)two pairs of perpendicular straight lines (b)two pairs of parallel straight lines (c)two pairs of straight lines which are equally inclined to each other (d)none of these

The condition that the pair of straight lines ax^(2)+2xy+by^(2)=0 are parallel is:

Find the separate equation of the following pair of straight lines 3x^(2)+2xy-y^(2)=0

If the pair of straight lines ax^(2)-2pxy-y^(2)=0and x^(2)-2qxy-y^(2)=0 are such that each pair bisects the angle between the other pair , then prove that pq=-1 .