If (h,k) be the point on the axis of the curve 2(x-1)^2+2(y-1)^2 = (x+y+2)^2 from where three distinct normal can be drawn, then h satisfies the condition --- a. h is less than 4 b. h is greater than 6 c. h is less than 8 d. None of these Pls. give answers with solution
Answer (1)
24th Sep, 2020
Hello,
2(x-1)^2+2(y-1)^2=(x+y+2)^2
√ (x-1)^2+(y-1)^2 = |x+y+2/√1+1|
It represents a Parabola having
Focus at (1,1) &
Directrix is x+y+2=0
The equation of the axis is y-1=1(x-1)
i.e y= x
Y^2= 4ax
a=√2
So, y^2=4(√2)x
h=k, since(h,k) is a point on the axis of the parabola
Let the point be (x1,0)
For three distinct normal,
X1>2a= 2√2
Since |X1|= √h^2+k^2 = √2|h|
Hence, 2√2=h√2
h >2
Since the solution h>2 is not in the options that you have mentioned ,
The answer is option d none of these
Hope it helps
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