question no. 11 from chapter conic sections NCERT class 11.
Answers
Answer:
Let us consider the equation of the required circle be (x – h)2 + (y – k)2 = r2
We know that the circle passes through points (2,3) and (-1,1).
(2 – h)2+ (3 – k)2 =r2 ……………..(1)
(-1 – h)2+ (1– k)2 =r2 ………………(2)
Since, the centre (h, k) of the circle lies on line x – 3y – 11= 0,
h – 3k =11………………… (3)
From the equation (1) and (2), we obtain
(2 – h)2+ (3 – k)2 =(-1 – h)2 + (1 – k)2
4 – 4h + h2 +9 -6k +k2 = 1 + 2h +h2+1 – 2k + k2
4 – 4h +9 -6k = 1 + 2h + 1 -2k
6h + 4k =11……………. (4)
Now let us multiply equation (3) by 6 and subtract it from equation (4) to get,
6h+ 4k – 6(h-3k) = 11 – 66
6h + 4k – 6h + 18k = 11 – 66
22 k = – 55
K = -5/2
Substitute this value of K in equation (4) to get,
6h + 4(-5/2) = 11
6h – 10 = 11
6h = 21
h = 21/6
h = 7/2
We obtain h = 7/2and k = -5/2
On substituting the values of h and k in equation (1), we get
(2 – 7/2)2 + (3 + 5/2)2 = r2
[(4-7)/2]2 + [(6+5)/2]2 = r2
(-3/2)2 + (11/2)2 = r2
9/4 + 121/4 = r2
130/4 = r2
The equation of the required circle is
(x – 7/2)2 + (y + 5/2)2 = 130/4
[(2x-7)/2]2 + [(2y+5)/2]2 = 130/4
4x2 -28x + 49 +4y2 + 20y + 25 =130
4x2 +4y2 -28x + 20y – 56 = 0
4(x2 +y2 -7x + 5y – 14) = 0
x2 + y2 – 7x + 5y – 14 = 0
∴ The equation of the required circle is x2 + y2 – 7x + 5y – 14 = 0
Step-by-step explanation:
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Answer:
Poulengey : (Slowly) There is something about her. It may be worth trying.
Robert : Oh, come on Polly! You must be out of your mind !
Poulengey :(Unmoved) What is wrong with it? The Dauphin is in Chinon, like a rat in a
corner, except that he won't fight. The English will take Orleans. He'll not be
able to stop them.
Robert : He beat the English the year before last at Montargis. I was with him.
Poulengey : But his men are cowed and now he can't work miracles. And I tell you that
nothing can save our side now but a miracle.
Robert Miracles are alright, Polly. The only difficulty about them is that they don't
happen nowadays.
Poulengey :I used to think so. I'm not so sure now. There is something about her. I think
the girl herself is a bit of a miracle. Anyhow, this is our last chance. Let's see
what she can do.
Robert : (Wavering) You really think that?
Poulengey : (Turning) Is there anything else left for us to think? Let's take a chance. Her
words have put fire into me.
Robert : (Giving up) Whew! You're as mad as she is.
Poulengey : (Obstinately) We want a few mad people now. See where the same ones have
landed us !
Robert : I feel like a fool. Still, if you feel sure...?
Poulengey : I feel sure enough to take her to Chinon unless you stop me.
Robert : Do you think I ought to have another talk with her ?
Poulengey :(Going to the window) Yes ! Joan, come up.
(Joan enters).
Q: after talking to poulengey what change do you notice in Robert?