wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Column 1: Information about curves
Column 2: Type of curves
Column - 3: eccentricity of the curves given in column - 1
Column1Column2Column3(I)The curve such that products(i)Circle(P)e=1of the distances of any of its tangent from two given pointsis constant can be(II)A curve for which the length(ii)Parabola(Q)e<1of the subnormal at any of it'spoint is equal to 2 and the curvepasses through (1,2) can be(III)A curve passes through (1,4) and(iii)Ellipse(R)e=0is such that the segment joining any point P on the curve and thepoint of intersection of the normalat P with the x-axis is bisected bythe y-axis. the curve can be(IV)A curve passes through (1,2) is(iv)Hyperbola(S)e>1such that the length of thenormal at any of its pointis equal to 2.
Which of the following options is the only correct combination?

A
(I)(i)(P)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(I)(i)(R)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(I)(iii)(Q)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
(I)(iv)(Q)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C (I)(iii)(Q)
(C)
(I) It is a very important property of ellipse and hyperbola p1p2=b2

(II)y(dydx)=2y22=2x+c
At x=1, y=2c=0
y2=4x which is a parabola.

(III) Equation of normal at P
(Yy)=1m(Xx)
Y=0, X=x+my
X=0, Y=yxm
Hence, x+my+x=02x+y(dydx)=0
(2x)dx+(y)dy=0
x2+y22=C
1+8=C [passes through (1, 4)]
x2+y22=9x29+y218=1 ellipse

(IV) length of normal
(x+myx)2+y2=4
m2=4y2y2dydx=4y2y4y2=x+c
x=1, y=4c=1
(x1)2+y2=4 circle.

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon