The length of the chord of the parabola y2=x which is bisected at the point (2,1) is?


a)51/2     b)4*31/2     c)3*31/2     d)2*51/2

2 years ago

Share

Answers : (1)

                                        

T = S1


y-0.5(x+2) = 1^2 - 2 = -1


 


2y - x - 2 = -2


or, x = 2y


 


Put in the equation,


 


y^2 = 2y


or, y = 0 , 2


x = 0, 4


Points where the line cuts the parabola = (0,0), (4,2)


 


Length = sqrt(4^2 + 2^2) = sqrt(16+4) = sqrt(20) = 2*sqrt(5)


 


Option (d)

2 years ago

Post Your Answer

More Questions On Analytical Geometry

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
the normal to the curve at P(x,y) meets the x axis at G. If the distance of G from the origin is twice the abscissa of P , then the curve is a) ellipse b) parabola c) ellipse or hyperbola
 
 
solution: for any curve the equation of normal at ( X1, Y1) (y- y1) = -1/m (x- X1) {where m = slope of tengent or say dy/dx at (x1, Y1) } normal meets the X axis at G.. so ( 0 - y1) = -1/m...
  img
Ajay Verma 8 months ago
 
but sir the answer says it can be both ellipse as well as hyperbola, so can u please prove this as an ellipse too.
 
vansh kharbanda 8 months ago
 
thank you
 
vansh kharbanda 8 months ago
If the distance between circumcentre and orthocentre of triangle whose vertices are (1,5) (2,3) (4,4) is k/√10 then sum of abscissa of points which are k distance away from the point (3,2)...
 
 
A (1,5) B (2,3) C (4,4) AB= √5 units BC=√5 units AC= √10 units Hence given triangle is right angled triangle ( AB2 + BC2 = AC2) at B Orthocenter is B only CIrcumcenter for...
  img
Harsh Patodia 2 months ago
If the vertices of triangles are placed at (0,0), (0,6), (6,0). The prove that the distance between the orthocentre and circumcentre is 3 root2.
 
 
Solution: As we know the.. orthocentre is the point of intersection of altitudes of the triangle... soo for right angle triangle.. orthocenter is the vertex itself on which right angle is...
  img
Ajay Verma 4 months ago
Dear sir I am having problem in this question Find a dot b and a cross b if- Avector=i cap + 2jcap +kcap and b magnitude is 3 along c vector=icap+jcap+kcap
 
 
Hi please evaluate dot and cross yourself. Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty
  img
Arun Kumar 5 months ago
If f(x) = |x-25| & g(x) = f(f(x)) then for x > 50, g ’ (x) is
 
 
Ans:Hello student, please find answer to your question For x > 50
  img
Jitender Singh 4 months ago
Given: [a/(b+c)] + [b(a+c)] + [c/(a+b)] = 1 Then What is the Value of : [a 2 /(b+c)] + [b 2 (a+c)] + [c 2 /(a+b)] ?
 
 
Hello student, Please find the response to your question below I think there is some data missing or some mistake in your question. whether it is b(a+c) or b/a+c also it is b 2 (a+c) or b 2...
  img
SHAIK AASIF AHAMED 3 months ago
 
We have (a+b+c)[ (a/b+c) + (b/c+a) + (c/a+b) ] = a^2/(b+c)+b^2/(c+a)+c^2/(a+b) + (a+b+c) Hence if (a/b+c) + (b/c+a) + (c/a+b) =1, the equation becomes a+b+c = a^2/(b+c)+b^2/(c+a)+c^2/(a+b) +...
 
mycroft holmes 3 months ago
 
Sir, Thankyou for the response so that i could post the accurate question as follows: [a/(b+c)] + [b / (a+c)] + [c/(a+b)] = 1 Then What is the Value of : [a 2 /(b+c)] + [b 2 / (a+c)] + [c 2...
 
Hari Eeshwar 3 months ago
View all Questions »