MHT CET · Maths · Pair of Lines
The line coincides with one of the lines given by then the value of is
- A
- B
- C
- D
Answer & Solution
Correct Answer
(C)
Step-by-step Solution
Detailed explanation
As \(y^2\) is absent in given equation
\(\therefore\) first line is \(5 x+y-1=0\) and second is \(a x+c=0\)
\((5 x+y-1)(a x+c)=0\)
\(5 a x^2+5 c x+a x y+c y-a x-c=0\)
\(5 a x^2+a x y+x(5 c-a)+c y-c=0\)
Given equation \(5 x^2+x y-k x-2 y+2=0\)
\(\therefore a=1 ; c=-2\)
\(\therefore-k=5 c-a\)
\(-k=5(-2)-1\)
\(-k=-10-1\)
\(K=11\)
\(\therefore\) first line is \(5 x+y-1=0\) and second is \(a x+c=0\)
\((5 x+y-1)(a x+c)=0\)
\(5 a x^2+5 c x+a x y+c y-a x-c=0\)
\(5 a x^2+a x y+x(5 c-a)+c y-c=0\)
Given equation \(5 x^2+x y-k x-2 y+2=0\)
\(\therefore a=1 ; c=-2\)
\(\therefore-k=5 c-a\)
\(-k=5(-2)-1\)
\(-k=-10-1\)
\(K=11\)
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