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Syllabus

_{1}N_{1}and S_{2}N_{2}b e the perpendiculars from the foci S_{1 }and S_{2}of an ellipse upon any tangent to the ellipse then prove that N_{1}and N_{2}lie on the auxillary circle and S_{1}N_{1 }:S_{2}N_{2}= b^{2}.^{2}=4ax and PQ is a focal chord. PT is a tangent at P and QN is a normal at Q. The minimum distance between PT and QN is equal to.?Q104. The focal chord of

y^{2}= 16xis tangent to (x- 6)^{2}+y^{2}=2 then the possible values of the slope of this chord area) 1, – 1 b) $\frac{-1}{2},2$

c) 2, $\frac{1}{2}$ d) $\frac{1}{2}$ , 2

[OPTIONS]:

A.-2.5

B.-2

C.-1.5

D.-1

P.S.The answer is A.-2.5.Just tell me how.

Solve this :Q. If (5, 12) and (24, 7) are the focii of an ellipse passing through origin, then the eccentricity of ellipse is :

$\left(\mathrm{a}\right)\frac{\sqrt{386}}{38}\left(\mathrm{b}\right)\frac{\sqrt{386}}{12}\left(\mathrm{c}\right)\frac{\sqrt{386}}{13}\left(\mathrm{d}\right)\frac{\sqrt{386}}{25}$

_{1}are eccentricities of a hyperbola and its conjugate, show that 1/e^{2 }+ 1/e_{1}^{2}= 1in Q such that PQ=d is :

(A) (r - d)sinq = b, (B) (r ± d)sinq = b, (C) (r - d)cosq = b, (D) (r ± d)cosq = b

^{2}+24x-40y+134=0x^2/4 +y^2=1

at the end

points of its major and minor axes is

Q103. If a tangent to the parabola y

^{2}= 4ax meet the X-axis in T and tangent at the vertex A in P and the rectangle TAPQ completed. The locus of Q isa) y

^{2}+ ax = 0 b) y^{2}– ax = 0c) x

^{2}+ ay = 0 d) x^{2}^{ }– ay = 0If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be 1/2, then length of the minor axis is ....................

(a) 3 (b) $\sqrt[4]{2}$

(c) 6 (d) None of these

44.The high melting point and insolubility in organic solvents of sulphanilic acid are due to its ....... structure[IIT JEE 1994](a) Simple ionic (b) Bipolar ionic

(c) Cubic (d) Hexagonal

^{1/2 }- 5 , which is parallel to the line 4x-2y+5=0lx + my + n =0 will touch tho parabolay^{2}= 4ax, if ________(a)

mn=al^{2}(b)lm=an^{2}(c)ln=am^{2}(d) (a)mn=al^{2}is tangent to the hyperbola x^{2}/a^{2}- y^{2}/b^{2}= - 1.Find the locus of the middle point of PQ.

$\frac{{x}^{2}}{25}+\frac{{y}^{2}}{16}=1$

y^{2}= 4axmaking an angleθwithx-axis is(a)

y=xcot θ +atanθ(b)x – ytanθ+acotθ(c)y = xtanθ+a cotθ(d) None of these