A foot of the normal from the point $(4,3)$ to a circle is $(2,1)$ and a diameter of the circle has the...
$begingroup$
A foot of the normal from the point $(4,3)$ to a circle is $(2,1)$ and a diameter of the circle has the equation $2x-y-2=0$.Then find the equation of the circle.
For the equation of the circle,we need to find the center and radius of the circle but from only the equation of the diameter,how should i find the center and the radius.Please suggest me some method.
analytic-geometry circle
asked Sep 20 '15 at 13:21
learner_avidlearner_avid
711618
$endgroup$
add a comment |
$begingroup$
A foot of the normal from the point $(4,3)$ to a circle is $(2,1)$ and a diameter of the circle has the equation $2x-y-2=0$.Then find the equation of the circle.
For the equation of the circle,we need to find the center and radius of the circle but from only the equation of the diameter,how should i find the center and the radius.Please suggest me some method.
analytic-geometry circle
asked Sep 20 '15 at 13:21
learner_avidlearner_avid
711618
$endgroup$
2
$begingroup$
Hint: if you extend the normal vector between the two given points it will pass through the center of the circle. But the center must also lie on the diameter.
$endgroup$
– lulu
Sep 20 '15 at 13:24
1
$begingroup$
@lulu,thank you,i got it.
$endgroup$
– learner_avid
Sep 20 '15 at 13:43
add a comment |
$begingroup$
A foot of the normal from the point $(4,3)$ to a circle is $(2,1)$ and a diameter of the circle has the equation $2x-y-2=0$.Then find the equation of the circle.
For the equation of the circle,we need to find the center and radius of the circle but from only the equation of the diameter,how should i find the center and the radius.Please suggest me some method.
analytic-geometry circle
asked Sep 20 '15 at 13:21
learner_avidlearner_avid
711618
$endgroup$
A foot of the normal from the point $(4,3)$ to a circle is $(2,1)$ and a diameter of the circle has the equation $2x-y-2=0$.Then find the equation of the circle.
For the equation of the circle,we need to find the center and radius of the circle but from only the equation of the diameter,how should i find the center and the radius.Please suggest me some method.
analytic-geometry circle
analytic-geometry circle
asked Sep 20 '15 at 13:21
learner_avidlearner_avid
711618
asked Sep 20 '15 at 13:21
learner_avidlearner_avid
711618
asked Sep 20 '15 at 13:21
learner_avidlearner_avid
711618
asked Sep 20 '15 at 13:21
learner_avidlearner_avid
711618
asked Sep 20 '15 at 13:21
learner_avidlearner_avid
711618
711618
2
$begingroup$
Hint: if you extend the normal vector between the two given points it will pass through the center of the circle. But the center must also lie on the diameter.
$endgroup$
– lulu
Sep 20 '15 at 13:24
1
$begingroup$
@lulu,thank you,i got it.
$endgroup$
– learner_avid
Sep 20 '15 at 13:43
add a comment |
2
$begingroup$
Hint: if you extend the normal vector between the two given points it will pass through the center of the circle. But the center must also lie on the diameter.
$endgroup$
– lulu
Sep 20 '15 at 13:24
1
$begingroup$
@lulu,thank you,i got it.
$endgroup$
– learner_avid
Sep 20 '15 at 13:43
2
2
$begingroup$
Hint: if you extend the normal vector between the two given points it will pass through the center of the circle. But the center must also lie on the diameter.
$endgroup$
– lulu
Sep 20 '15 at 13:24
$begingroup$
Hint: if you extend the normal vector between the two given points it will pass through the center of the circle. But the center must also lie on the diameter.
$endgroup$
– lulu
Sep 20 '15 at 13:24
1
1
$begingroup$
@lulu,thank you,i got it.
$endgroup$
– learner_avid
Sep 20 '15 at 13:43
$begingroup$
@lulu,thank you,i got it.
$endgroup$
– learner_avid
Sep 20 '15 at 13:43
add a comment |
1 Answer
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Write eqn. of the normal from the points given.then solve it with eqn. Of diameter you will get the centre and write the eqn. By finding the radius by distance formula bw the centre and foot of normal
answered Oct 12 '15 at 16:06
user279579user279579
1
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add a comment |
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$begingroup$
Write eqn. of the normal from the points given.then solve it with eqn. Of diameter you will get the centre and write the eqn. By finding the radius by distance formula bw the centre and foot of normal
answered Oct 12 '15 at 16:06
user279579user279579
1
$endgroup$
add a comment |
$begingroup$
Write eqn. of the normal from the points given.then solve it with eqn. Of diameter you will get the centre and write the eqn. By finding the radius by distance formula bw the centre and foot of normal
answered Oct 12 '15 at 16:06
user279579user279579
1
$endgroup$
add a comment |
$begingroup$
Write eqn. of the normal from the points given.then solve it with eqn. Of diameter you will get the centre and write the eqn. By finding the radius by distance formula bw the centre and foot of normal
answered Oct 12 '15 at 16:06
user279579user279579
1
$endgroup$
Write eqn. of the normal from the points given.then solve it with eqn. Of diameter you will get the centre and write the eqn. By finding the radius by distance formula bw the centre and foot of normal
answered Oct 12 '15 at 16:06
user279579user279579
1
answered Oct 12 '15 at 16:06
user279579user279579
1
answered Oct 12 '15 at 16:06
user279579user279579
1
answered Oct 12 '15 at 16:06
user279579user279579
1
1
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2
$begingroup$
Hint: if you extend the normal vector between the two given points it will pass through the center of the circle. But the center must also lie on the diameter.
$endgroup$
– lulu
Sep 20 '15 at 13:24
1
$begingroup$
@lulu,thank you,i got it.
$endgroup$
– learner_avid
Sep 20 '15 at 13:43