Question
Let L_1 be the length of the common chord of the curves x^2+y^2=9 and y^2=8 x, and L_2 be the length of the latus rectum of y^2=8 x, then:
BITSAT
Mathematics
Parabola
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. L _1 L _2
- B. L _1= L _2
- C. L _1 L _2
- D. L _1 ~L _2 = 2
Answer
C. L _1 L _2
Step-by-step solution
We have : x^2+(8 x)=9 x^2+9 x-x-9=0 x(x+9)-1(x+9)=0 (x+9)(x-1)=0 x=-9,1 for x=1, y= 2 2 x = 2 2 (2 2 +2 2 )^2+(1-1)^2 =4 2 L _n= Length of latus rectum =4 a=4 2=8 L _1 L _2
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