If two lines represented by `x^2(tan^2theta+cos^2theta)-2xytantheta+y^2sin^2theta=0` make angles `alpha, beta` with x-axis thenA. 4B. 3C. 2D. none of these

If two lines represented by `x^2(tan^2theta+cos^2theta)-2xytantheta+y^

1.	If two lines represented by `x^2(tan^2theta+cos^2theta)-2xytantheta+y^2sin^2theta=0` make angles `alpha, beta` with x-axis thenA. 4B. 3C. 2D. none of these
Answer» Correct Answer - C Let `m_(1)` and `m_(2)` be the slopes of the lines given by `x^(2)(tan^(2)theta+cos^(2)theta)-2xy tan theta +y^(2)sin^(2)theta=0`. Then, `m_(1)+m_(2)=(2tan theta)/(sin^(2)theta)=2sec theta" cosec "theta` and `m_(1)m_(2)=(tan^(2)theta+cos^(2)theta)/(sin^(2)theta)=sec^(2)theta+cot^(2)theta` `therefore" "m_(1)-m_(2)=sqrt((m_(1)+m_(2))^(2)-4m_(1)m_(2))` `rArr" "m_(1)-m_(2)=sqrt(4sec^(2)theta" cosec"^(2)theta-4(sec^(2)theta+cot^(2)theta))` `rArr" "m_(1)-m_(2)=sqrt(4sec^(2)theta(1+cot^(2)theta)-4(sec^(2)theta+cot^(2)theta))` `rArr" "m_(1)-m_(2)=2sqrt(sec^(2)thetacot^(2)theta-cot^(2)theta)` `rArr" "m_(1)-m_(2)=2sqrt(cot^(2)theta(sec^(2)theta-1))=2`

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`