Question

Co-ordinate Geometry JEEMain(ref. attachment)
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Answer 1

Answer:

21.

Step-by-step explanation:

Let,

A ----> (2,-3)

B ----> (-5,6)

Point on Y axis , P ----> (0, y )

M1 : M2 : : l : m.

Assume, m = 1.

So,

M1 : M2 : : l : 1.

P (0, y ) -----> { [(l )(-5) + (1 )(2 )] / [ l + 1 ] } , { [(l )(6 ) + (1 )(-3 )] / [ l + 1 ] }

------> { [-5l + 2] / [ l + 1 ] } , { [6l - 3] / [ l + 1 ] }

Comparing both sides,

0 = [-5l + 2] / [ l + 1 ]

-5l + 2 = 0

-5l = -2

l = -2/-5 = 2/5.

So,

M1 / M2 = l / 1 = (⅖)/1 = 5/2

So,

M1 : M2 : : 5 : 2

i.e.,

l = 5

m = 2.

To find,

l² - m² = 5² - 2² = 25 - 4 = 21.

P.S. :

I'm in class 10. So, I'm not sure if it is correct. We're currently studying Coordinate geometry at school. So, I tried to solve it with that knowledge only. Hope this helps !!!!

You're preparing for JEE ????!!!! OMG... Anyway, best of luck...! You can crack it !!!!