Plz solve question 2.

# Doubt from straight lines

Take a parametric coordinate in curve reflection of that about line will give other point find locus of point..

\textbf {jee advanced 2015 type problem}

How to take the parametric coordinate??

See easy way without taking parametric also

x=0,y=0 , x=a,y=a satisfying reflect them along line u will get point nd satisfy in option u will get ans d option

Or

x=at^2, y=at^3

U may gooped up in calculation in parametric form i think so gave other approch to

Yes I solved it the first way, but thought that it would be easier if parametric coordinates are known. But as you said it is lengthy.

Family of lines try partial differentiation mthd

Can you pls elaborate, I'm kinda weak here.

I m sorry that may be a mthd but i hvnt tried the question is going for homogenization

y=mx+c

\dfrac{y-mx}{c }=1

Then 1 degree term in given question write this in place of 1

Now coefficient of x^2+y^2=0

First reflect across x-axis, so the y- coordinate changes sign and we are dealing with the curves

ay^2=x^3 and x-y=a

Now let X=x-a, Y=y i.e. translate origin of axes to (a,0). Then we have to reflect aY^2 = (X+a)^3 across X-Y=0

Now, the reflected curve is aX^2 = (Y+a)^3 i.e. a(x-a)^2 = (y-a)^3

Now reflect this curve across x- axis and we get a(x-a)^2 = (a-y)^3

#18: As suggested by @Sneha_2021 use homogenization. Take the chord as y=mx+c so that \dfrac{y-mx}{c}=1

Hence 2x^2+3y^2 - 5x \left( \dfrac{y-mx}{c} \right)=0 or (5m+2c)x^2-5xy+3cy^2=0 represents the pair of lines joining origin to the point of intersection of the chord with the ellipse.

and since the pair of lines are orthogonal we have coeff of x^2+coeff of y^2=0 i.e. 5m+5c =0 or m+c=0

Hence the equation of the chord is of the form y=m(x-1) which always passes through (1,0)

2 may be

#hint

x^2+y^2<16

Where x=\alpha ,y=\alpha+1

Now put value of \alpha hit nd trail

2 ans u will get

But answer is c....

Oo sheesh i mean only 2 point which will not satisfy the condition

The condition

Will be x^2+y^2>16

Ans is 19