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The equation 8x^2+8xy+2y^2+26x+13y+15=0 ...

The equation `8x^2+8xy+2y^2+26x+13y+15=0` represents a pair of straight lines. The distance between them is

A

`(7)/(sqrt(5))"units"`

B

`(7)/(2sqrt(5))"units"`

C

`sqrt((7)/(5))"units"`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
The distance between the parallel straight lines given by `ax^2+2hxy+by^2+2gx+2fy+c=0` is given by
`d=2(sqrt(g^2-ac))/(a(a+b))`
Here , `a=8,b=2,c=15and g=13`
`therefore` Required distance `=2(sqrt(169-120))/(80)=2xx(7)/(1sqrt(5))=(7)/(2sqrt(5))`units.
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PAIR OR STRAIGHT LINES -PRACTICE EXCERCISE (Excercise 1) (Topical Problems) (General Equation of Second Degree)
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  3. If lambdax^(2)-10xy+12y^(2)+5x-16y-3=0, represents a pair of straight ...

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  4. If ax^2-y^2+4x-y=0 represents a pair of lines , then a is equal to

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  5. The value of lambda for which the equation x^2-y^2 - x - lambda y - ...

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  6. The value of 'p' for which the equation x^2+pxy+y^2-5x-7y+6=0 represen...

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  7. If the equation kx^2-2xy-y^2-2x+2y=0 represents a pair of lines , then...

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  8. The equationof the pair of straight lines perpendicular to the pair 2x...

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  9. The lines represented by the equation x^2-y^2-x+3y-2=0 are

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  10. If the lines x^2+2x y-35 y^2-4x+44 y-12=0 and 5x+lambday-8 are concurr...

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  11. In order to eliminate the first degree terms from the equation 2x^2+4x...

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  12. The equation x^(2)+2sqrt(ab)xy+by^(2)+2 gx+2fy+c=0 represents a pa...

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  13. If the lines joining the origin to the points of intersection of the ...

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

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  15. The equation 8x^2+8xy+2y^2+26x+13y+15=0 represents a pair of straight ...

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  16. If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two str...

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  18. The equation ax^2+by^2+cx+cy=0 c !-=0 represents a pair of straight li...

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  20. The pairs of straight lines x^2-3xy+2y^2=0 and x^2-3xy+2y^2+x-1 form a

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