Question

If the slopes of the lines kx^2-7xy+y^2=0 differ by 3, then k is:
(a) 5
(b) 6
(c) 7
(d) 10

Answer 1

Given: line - kx^2-7xy+y^2=0, slopes differ by 3

To find: k

Solution: The equation representing two different lines is in the form ax^2+ 2hxy+ by^2 = 0. This is also called general second degree equation in x and y.

for this equation, sum of the slopes = -2h/b

and product of slopes = a/b

Now we are given an equation kx^2-7xy+y^2=0.

On comparing, with the general second degree equation we will get

a= k, b= 1, h= -7/2

let the slopes of this equation be m1 and m2

m1+ m2 = -2h/b= (-2×-7/2)/1 = 7

m1×m2= a/b = k/1 = k

Also it is given that slopes differ by 3

Therefore, m1- m2 = 3

(m1- m2) ^2 = (m1+m2) ^2 -4m1×m2

3^2 = 7^2 - 4×k

4k= 49-9

k= 10

Therefore, the value of k will be d) 10.

Answer 2

Answer:-

The correct alternative is option (d) 10.

[ Steps with soln is there in above pic plz go through it]

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