If a point P is taken on xy=2 and then a...

If a point `P` is taken on `xy=2` and then a normal is drawn from `P` on the ellipse `(x^(2))/6+(y^(2))/3=1` which is perpendicular to `x+y=8`, then `P` is

A

`(1,2)`

B

`(-1,-2)`

C

`(2,1)`

D

`(-2,-1)`

Text Solution

Verified by Experts

The correct Answer is:

B, C

`:' sqrt(6)xsectheta-sqrt(3)ycosectheta=3` is equation of normal,
then, slope `=(-sqrt(6)sectheta)/(-sqrt(3)cosectheta)=sqrt(2) tan theta`
Given, `sqrt(2)tantheta=+1`
`impliestantheta=1/(sqrt(2))`
`:.` normal is `x-y=1`
Let `P(h, 2/h)`
`implies h-2/h=1`
`impliesh^(2)h-2=0`
`impliesh=2` or `-1`

Topper's Solved these Questions

STRAIGHT LINE
FIITJEE|Exercise NUMERICAL BASED|4 Videos
TIPS
FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

Similar Questions

Explore conceptually related problems

If the normal from the point P(h,1) on the ellipse (x^(2))/(6)+(y^(2))/(3)=1 is perpendicular to the line x+y=8 ,then the value of h is

If the tangents drawn from a point p to the ellipse 4x^(2)+9y^(2)-24x+36y-72=0 are perpendicular,then locus of p is

The equation of the normal at the point P (2, 3) on the ellipse 9x^(2) + 16y^(2) = 180 , is

Tangents are drawn from the point P(3,4) to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 touching the ellipse at points A and B.

If from a point P, tangents PQ and PR are drawn to the ellipse (x^(2))/(2)+y^(2)=1 so that the equation of QR is x+3y=1, then find the coordinates of P.

If the lines (p-q)x^2+2(p+q)xy+(q-p)y^2=0 are mutually perpendicular , then

the locus of the foot of perpendicular drawn from the centre of the ellipse x^(2)+3y^(2)=6 on any point:

If N is the foot of the perpendicular drawn from any point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (a>b) to its major axis AA' then (PN^(2))/(AN A'N) =

Tangents are drawn from a point P on the line y=4 to the circle x^(2)+y^(2)=25 .If the tangents are perpendicular to each other,then coordinates of P are

FIITJEE-TEST PAPERS-MATHEMATICS

If alpha and beta are roots of equation 3/4"sin"((theta)/9)=sin^(3)the...
Text Solution
|
Volume of parallelepiped determined by vectors bara,barb and barc is 5...
Text Solution
|
If a point P is taken on xy=2 and then a normal is drawn from P on the...
Text Solution
|
A circle S having centre (alpha, beta) intersect at three points A, B ...
Text Solution
|
If f(x)=||x-1|+|x-3|-|2x-1||+||x-1|+|x-3|+|2x-1||, then
Text Solution
|
If intcos2018xsin^(2016)x dx=f(x)+c, where f(0)=0, then
Text Solution
|
In a /\ABC if a^(2)-b^(2)-c^(2)+(x-2)bc=0 then x be equal to
Text Solution
|
If f(x)={b^(2)+(a-1)b+2}x-int(sin^(2)x+cos^(4)x)dx be an increasing fu...
Text Solution
|
Let f(x) be a continuous function which takes positive values for xge0...
Text Solution
|
If x+y=3 is tangent at (2,1) on hyperbola, intersects asymptotes at A ...
Text Solution
|
If x^(2)+y^(2)=16 is director circle of locus of centre of a moving el...
Text Solution
|
If theta is acute angle of intersect between two curves x^(2)+5y^(2)=6...
Text Solution
|
If 8 harmonic means are inserted between two numbes a and b (altb) suc...
Text Solution
|
If f(x)=sum(i=1)^(oo) x/({(i-1)x+1}(ix+1)), then f(2017)+f(1/2017) is ...
Text Solution
|
If tangent is drawn at (x(1), y(1)) on the hyperbola (x^(2))/4-(y^(2))...
Text Solution
|
If int(0)^(x)((t^(3)+t)dt)/((1+3t^(2)))=f(x), then int(0)^(1)f^(')(x) ...
Text Solution
|
If y=f(x) is solution of differentiable equation (dy)/(dx)=y/x((1-3x^(...
Text Solution
|
If 5x(1+ 1/(x^(2)+y^(2)))=12 and 5y(1- 1/(x^(2)+y^(2)))=4 AAx,yepsilon...
Text Solution
|
If a tangent on ellipse at A(1,1) intersect its directrix at B(7,-6) a...
Text Solution
|
let f(x)=(cos^-1(1-{x})sin^-1(1-{x}))/sqrt(2{x}(1-{x})) where {x} deno...
Text Solution
|