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Syllabus

_{1}and r_{2}and the radii of smallest and largest circles which passes through (5, 6) and touches the circle (x - 2)^{2}+ y^{2}= 4, then r_{1}r_{2}is .$a)\frac{4}{41}\phantom{\rule{0ex}{0ex}}b)\frac{41}{4}\phantom{\rule{0ex}{0ex}}c)\frac{5}{41}\phantom{\rule{0ex}{0ex}}d)\frac{41}{6}$

^{2}= 2x is^{2}at (2 ,4 ) is :(a) $\left(-\frac{16}{5},\frac{27}{10}\right)$ (b) $\left(-\frac{16}{7},\frac{53}{10}\right)$ (c) $\left(-\frac{16}{5},\frac{53}{10}\right)$ (d) none of these

84) The locus of poles of normal chords of the parabola y^{2}= 4ax is1) (x + 2a) y^{2}= 4a^{3}2) (x + 2a) y^{2}+ 4a^{3}= 0 3) (x – 2a) y^{2}= 4a^{3}4) (x – 2a) y^{2}+ 4a^{3}= 05) Through the vertex O of the parabola y^{2}= 4ax a perpendicular is drawn to any tangent meeting it at P and the parabola at Q. Then OP.OQ = ___1) a^{2}2) 2a^{2 }3) 3a^{2}4) 4a^{2}1)The line 9x + y – 28 = 0 is the chord of contact of the point P(h,k) with respect to the circle2x

^{2}+ 2y^{2}- 3x + 5y – 7 = 0 then P isa)(3, -1) b) (3, 1) c) (-3, 1) d) no position of pQ6. The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x

^{2}+ y^{2}= 9 is :(a) (3/2, 1/2 ) (b) (1/2, 3/2 )

(c) (1/2, 1/2) (d) $\left(\frac{1}{2}\pm \sqrt{2}\right)$

7.The length of the latus-rectum of the parabola x = ay

^{2}+ by + c is$\text{(a)}\frac{\text{a}}{\text{4}}\text{(b)}\frac{\text{a}}{\text{3}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\text{(c)}\frac{\text{1}}{\text{a}}\text{(d)}\frac{\text{1}}{\text{4a}}$

22) An arch is in the shape of a parabola whose axis is vertically downwards and measures 80 mts across its bottom on the ground. Its highest point is 24 mts. The measure of the horizontal beam across its cross section at a height of 18 mts is __

1) 50 2) 40 3) 45 4) 60Six points (x

_{i},y_{i}), i=1,2,..6 are taken on the circle ${x}^{2}+{y}^{2}=4$ such that $\sum _{\mathrm{i}=1}^{6}{\mathrm{x}}_{\mathrm{i}}=8\mathrm{and}\sum _{\mathrm{i}=1}^{6}{\mathrm{y}}_{\mathrm{i}}=4$The line segment joining orthocentre of a triangle made by any three points and the centroid of the triangle made by other three points passes through a fixed points (h,k) , then h+k is

a)1

b) 2

c)3

d) 4

Ans: C.

How?

$a)6\phantom{\rule{0ex}{0ex}}b)12\phantom{\rule{0ex}{0ex}}c)6\sqrt{2}\phantom{\rule{0ex}{0ex}}d)24-4\sqrt{2}$

Q12. The value of 'c' for which the set, {(x , y) | x

^{2}+ y^{2}+ 2x $\le $1}$\u2312${ (x, y) [ x – y + c $\ge $0} contains only one point in common is :(a) $\left(-\infty ,-1\right)$ $\u2312$ [ 3, $\infty $) (b) { – 1, 3}

(c) { – 3} (d) { – 1}

Q. If a tangent line at a point P on a parabola makes angle $\alpha $ with its focal distance, then angle between the tangent and axis of the parabola is -

(A) $\alpha $

(B) $\alpha $/2

(C) 2$\alpha $

(D) 90$\xb0$

(a) y

^{2}= 4 ( 3-x ) (b) y^{2}= 4x -4(b) both (a) and (b) (d) none of these

8. Coordinates of the focus of the parabola x

^{2}- 4x - 8y - 4 = 0 are(a) (0,2) (b) (2,1)

(c) (1,2) (d) (-2,-1)

^{2}+ y^{2}- 6x - 16 = 0 and x^{2}+ y^{2}- 8y - 9 = 0 is^{2}- 2y + 4x - 2xy = 0 as its normal & passing through the point (2,1) is$\mathbf{43}\mathbf{.}Letx,yberealvariablesatisfyingthe{x}^{2}+{y}^{2}+8x-10y-40=0.Leta=max\left\{\sqrt{\left(x+{2}^{2}\right)+{\left(y-3\right)}^{2}}\right\}andb=min\left\{\sqrt{\left(x+{2}^{2}\right)+{\left(y-3\right)}^{2}}\right\},then\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(a\right)a+b=18\left(b\right)a+b=4\sqrt{2}\phantom{\rule{0ex}{0ex}}\left(c\right)a-b=4\sqrt{2}\left(d\right)a.b=73$

love Vashikaran Specialist Baba Ji +91-8872522276

and i. passing through the point (-4,5).

(a) x = 0

(b) 24x + 7y = 0

(c) 7x + 24y = 0

(d) 7x - 24y = 0

$AvariablecircleChastheequation{x}^{2}+{y}^{2}-2({t}^{2}-3t+1)x-2({t}^{2}+2t)y+t=0,wheretisaparameter.IfthepowerofpointP(a,b)w.r.tthecircleCiscons\mathrm{tan}tthentheorferedpair(a,b)is\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(A\right)\left(\frac{1}{10},-\frac{1}{10}\right)\left(B\right)\left(-\frac{1}{10},\frac{1}{10}\right)\left(C\right)\left(\frac{1}{10},\frac{1}{10}\right)\left(D\right)\left(-\frac{1}{10},-\frac{1}{10}\right)$

Why did you derivate f(m) and how did alpha equals minus beta ?

Again why f(alpha).f(-aplha) less than zero ?

Please help me out....

(a) 4x + 3y = 0

(b) 4x - 3y = 0

(c) 4x + 3y - 24 = 0

(d) 4x + 3y - 12 = 0

Q51. The equation of the chords of length 5 and passing through the point (3, 4) on the circle 4x

^{2}+ 4y^{2}– 24x – 7y = 0 are(a) 4x + 3y = 0 (b) 4x – 3y = 0

(c) 4x + 3y – 24 = 0 (d) 4x + 3y – 12 = 0

Ans: B.

4√2and the length of latus rectum is4.^{2}+ y^{2}+ 20(x+y) + 20 = 0. The equation of the pair of tangents is5. The equation of the circle which is touched by y=x, has its centre on the positive directin of the x-axis & uts off a chord of length 2 units along the line $\sqrt{3}y-x=0$ is;

(a) x

^{2}+y^{2}-4x+2=0 (b) x^{2}+y^{2}-8x+8=0(c) x

^{2}+y^{2}-4x+1=0 (d) x^{2}+y^{2}-4y+2=0Ans : option (D).

Q. A chord of a circle divides the circle into two parts such that the squares inscribed in the two parts have areas 16 and 144 square units. The radius of the circle, is

(A) $2\sqrt{10}$

(B) $6\sqrt{2}$

(C) 9

(D) $\sqrt{85}$

Q. What is the equation of the parabola having its axis parallel to x-axis and which passes through the points (l, 2), (—1,3) and (-2, 1)?

$\mathbf{6}\mathbf{.}FromthepointA\left(0,3\right)inthecircle{x}^{2}+4x+{\left(y-3\right)}^{2}=0achordABisdrawnextendedtoapointMsuchthatAM=2AB.TheequationofthelocusofMis:\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(a\right){x}^{2}+8x+{y}^{2}=0\left(b\right){x}^{2}+8x+{\left(y-3\right)}^{2}=0\phantom{\rule{0ex}{0ex}}\left(c\right){\left(x-3\right)}^{2}+8x+{y}^{2}=0\left(d\right){x}^{2}+8x+8{y}^{2}=0$