Column 1, 2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively. Column 1 Column 2 Column 3 (I) x^2+y^2=a^2 (i) my=m^2x+a (Q) (a/m^2,{2a}/m) (II) x^2+a^2y^2=a^2 (ii) y=mx+a\sqrt{m^2+1} (Q) ({{-ma}/\sqrt{m^2+1},a/\sqrt{m^2+1}) (III) y^2=4ax (iii) y=mx+\sqrt{a^2m^2-1} (R) ({-a^2m}/\sqrt{a^2m^2+1},1/\sqrt{a^2m^2+1}) (IV) x^2-a^2y^2=a^2 (iv) y=mx+\sqrt{a^2m^2+1} (S) ({-a^2m}/\sqrt{a^2m^2-1},{-1}/\sqrt{a^2m^2-1}) If a tangent to a suitable conic (Column 1) is found to be y=x+8 and its point of contact is (8,16), then which of the following options is the only CORRECT combination ? [JEE Adv 2017 P1]

Correct Answer is : (III) (i) (P)

Parabola

Section: Mathematics

Question : 12 of 31

Marks: +1, -0

Column 1, 2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.

Column 1

Column 2

Column 3

(I) x2+y2=a2

(i) my=m2x+a

(Q)(

)

(II) x2+a2y2=a2

(ii) y=mx+a√m2+1

(Q) (

−ma

√m2+1

)

(III) y2=4ax

(iii) y=mx+√a2m2−1

(R) (

−a2m

√a2m2+1

)

(IV) x2−a2y2=a2

(iv) y=mx+√a2m2+1

(S) (

−a2m

√a2m2−1

−1

√a2m2−1

)

If a tangent to a suitable conic (Column 1) is found to be y=x+8 and its point of contact is (8,16), then which of the following options is the only CORRECT combination ?

[JEE Adv 2017 P1]

(III) (ii) (Q)
(II) (iv) (R)
(I) (ii) (Q)
(III) (i) (P)

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