Question

Answer for 25 points

Question for Jee Aspirants.

Jee Advanced Question.

Correct answer will be marked as brainliest.

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Answer 1

heya friend

For a general equation representing a pair of straight lines, the point of intersection is given as:

For a general equation representing a pair of straight lines, the point of intersection is given as:( (hf-bg)/ab-h^2), (gh-af/ab-h^2) )

For a general equation representing a pair of straight lines, the point of intersection is given as:( (hf-bg)/ab-h^2), (gh-af/ab-h^2) )Hence the square of distance of point of intersection from the origin is given as, sum of squares of x and y coordinates of the point of intersection.

For a general equation representing a pair of straight lines, the point of intersection is given as:( (hf-bg)/ab-h^2), (gh-af/ab-h^2) )Hence the square of distance of point of intersection from the origin is given as, sum of squares of x and y coordinates of the point of intersection.(hf-bg)/ab-h^2)^2 + (gh-af/ab-h^2)^2

Answer 2

Solution :-

In the attachment

Things used while answering :-

A general solution for pair of lines

→ ax² + 2hxy + by² + 2gx + 2fy + c = 0

This can be written as the multiplication of two parallel straight line.

→ (a₁x + b₁y + c₁)(a₁x + b₁y + c₂) = 0

→ a₁²x² + 2a₁b₁xy + b₁²y² + a₁(c₁ + c₂)x

+ b₁(c₁ + c₂)y + c₁c₂

So by comparison we get the values :-

a = a₁²

b = b₁²

h = a₁b₁

2g = a₁(c₁ + c₂)

2f = b₁(c₁ + c₂)

c = c₁ c₂

For further please refer solution