The combined equation of the pair of lines through the point (1, 0) and perpendicular to the lines represented by `2x^(2)-xy-y^(2)=0`, isA. `2x^(2)-xy-y^(2)-x+y-1=0`B. `2y^(2)+xy-x^(2)+2x-y-1=0`C. `2y^(2)+xy-x^(2)-x-xy+2=0`D. none of these

The combined equation of the pair of lines through the point (1, 0) an

1.	The combined equation of the pair of lines through the point (1, 0) and perpendicular to the lines represented by `2x^(2)-xy-y^(2)=0`, isA. `2x^(2)-xy-y^(2)-x+y-1=0`B. `2y^(2)+xy-x^(2)+2x-y-1=0`C. `2y^(2)+xy-x^(2)-x-xy+2=0`D. none of these
Answer» Correct Answer - B The combined equation of the pair of lines through the origin and perpendicular to the lines given by `2x^(2)-xy-y^(2)=0 ` is `2y^(2)+xy-x^(2)=0`. Shifting the origin at (1, 0), the equations of the required lines are `2y^(2)+(x-1)y-(x-1)^(2)=0` or, `2y^(2)+xy-x^(2)+2x-y-1=0`

The lines represented by the equation `ax^(2)+2bxy+hy^(2)=0` are mutually perpendicular ifA. `a+b=0`B. `b+h=0`C. `h+a=0`D. `ah=-1`
If acute angle between lines `x^(2)-2hxy+y^(2)=0` is `60^(@)` then `h=`A. `-2`B. `+-2`C. `2`D. `sqrt(3)`
The angle between the lines `2x^2-7x y+3y^2=0`is`60^0`2. `45^0`3. `tan^(-1)(7//6)`4. `30^0`A. `60^(@)`B. `45^(@)`C. `tan^(-1)((7)/(6))`D. `30^(@)`
Find the value of `a`for which the lines represented by `a x^2+5x y+2y^2=0`are mutually perpendicular.
The two lines represented by `3a x^2+5x y+(a^2-2)y^2=0`are perpendicular to each other fortwo values of `a`(b) afor one value of `a`(d) for no values of `a`A. two values of aB. for one value of aC. for one value of aD. for no value of a
If acute angle between lines `ax^(2)+2hxy+by^(2)=0` is `(pi)/6`, then `a^(2)+14ab+b^(2)=`A. `4h^(2)`B. `8h^(2)`C. `12h^(2)`D. `16h^(2)`
If acute angle between lines `ax^(2)+2hxy+by^(2)=0` is congruent to that between lines `2x^(2)-5xy+3y^(2)=0` and `k(h^(2)-ab)=(a+b)^(2)` then `k=`A. `-(10)^(2)`B. `(-10)^(2)`C. `-10`D. `10`
If acute angle between lines `ax^(2)+2hxy+by^(2)=0` is `(pi)/4`, then `4h^(2)=`A. `a^(2)+4ab+b^(2)`B. `a^(2)+6ab+b^(2)`C. `(a+2b)(a+3b)`D. `(a-2b)(2a+b)`
The lines `a^2x^2+bcy^2=a(b+c)xy` will be coincident , ifA. `a=b`B. `b=c`C. `c=a`D. `b^(2)=ac`
Find the measure of the acute angle between the lines represented by `(a^(2) - 3b^(2)) x^(2) + 8abxy + (b^(2) - 3a^(2)) y^(2) = 0.`A. `(pi)/6`B. `(pi)/4`C. `(pi)/3`D. `(pi)/2`