QJEEM24Ma9fde: JEE Main 2024 Mathematics - Class 11 JEEM24Ma9fde Solution: Four distinct points and lie on a circle for equal to :

Question

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Four distinct points

(2 k, 3 k),(1,0),(0,1)

and

(0,0)

lie on a circle for

k

equal to :

Accepted Answer

$(2 k, 3 k)$ will lie on circle whose diameter is $A B$ .

JEE Main 2024 (Online) 27th January Morning Shift Mathematics - Circle Question 24 English Explanation

$\begin{aligned} (x - 1) (x) + (y - 1) (y) = 0 \\ x^{2} + y^{2} - x - y = 0 .... (i) \end{aligned}$

Satisfy (2k, 3k) in (i)

$\begin{aligned} (2 k)^{2} + (3 k)^{2} - 2 k - 3 k = 0 \\ 13 k^{2} - 5 k = 0 \\ k = 0, k = \frac{5}{13} \\ hence k = \frac{5}{13} \end{aligned}$

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