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`representtwo pairs of perpendicular straight linestwo pairs of parallel straight linestwo pairs of straight lines which are equally inclined to each othernone of theseA. two pair of perpendicular straight linesB. two pairs of parallel straight linesC. two pairs of straight lines which are equally inclined to each otherD. None of these

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`rep

1.	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`representtwo pairs of perpendicular straight linestwo pairs of parallel straight linestwo pairs of straight lines which are equally inclined to each othernone of theseA. two pair of perpendicular straight linesB. two pairs of parallel straight linesC. two pairs of straight lines which are equally inclined to each otherD. None of these
Answer» Correct Answer - 3 The given equations are `a^(2)x^(2)+2h(a+b)xy+b^(2)y^(2)=0` (1) and `ax^(2)+2hxy+by^(2)=0` (2) The equation of the bisectors of the angles between the lines represented by (1) is `(x^(2)-y^(2))/(a^(2)-b^(2))=(xy)/(h(a+b))` or `(x^(2)-y^(2))/(a-b)=(xy)/(h)` which is the same as the equation of bisectors of the angles between the line pair (2). thus , two line pairs are equally inclined to each other.

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`