
Let 2x2+y23xy=0 be the equation of a pair of tangents from origin O to a circle of radius 3 with center in the first quadrant. If A is one of the points of contact, Find the length OA ...

let a,b,c,d represent coplanar vectors and sin(A)a + 2sin(2B)b + 3sin(3C)c  4d = 0 then find the least value of sin(A)^2 +sin(2B)^2 + sin(3C)^2 is.... 1. 7/8 2. 8/7 3. 1 4. 2/3 ...

The tangent at a point C of a circle and diameter AB when extended intersect at P. If ∠PCA = 110° , find ∠CBA. a) 70° b) 105° c) 110° d) 120° ...

Q 17. The locus of the vertices of the family of parabolas y=a3x2/3+ a2x 2a is (1) xy= 105/64 (2) xy= 3/4 (3) xy= 35/16 (4) xy=64/105 ...

Let d be the perpendicular distance from the center of the ellipse x2/a2 + y2/b2 = 1 to the tangent drawn at a point P on the ellipse. If F' and F'' are the two foci of the ellipse , then show that (PF'  PF'')2= 4a2[ 1 (b2/ ...

If a,c,b are in G.P then the line ax+by+c=0 (A) has a fixed direction (B) always passes through a fixed point (C) forms a triangle whose area is constant (D) none of these ...

Prove that two of the straight lines represented by equation ax^3 + bx^2y + cxy^2 + dy^3 =0 will be at right angled if a^2 + ac + bd + d^2 =0. ...

22. A straight line is drawn from the point(1,0) to the curve x2+y2+6x10y+1=0, such that the intercept made on it by the curve subtends a right angle at the origin. Find the equations of the line. 23. Determine the range of ...

Q) The point on the hyperbola x2/24  y2/18 = 1 which is nearest to the line 3x + 2y + 1 = 0 is (A) (6,3) (B) (6,3) (C) (6,3) (D) (6,3) Acc. to me.. we take any point (asecθ , btanθ) on the hyperbola and find its perpen ...

1.the radius of the circle whose centre is[4,0] and which cuts the parabola y2=8x at A and B such that its common chord AB subtends a right angle at the vertex of the parabola is equal to a.4 b.3 c. 18 d.5 2.a normal is draw ...

prove that the polars of any point with respect to a system of coaxal circles all pass through a fixed point and that the two points are equidistant from the radical axis and subtend a right angle at a limiting point of the s ...

if the point [3,4] lies on the locus of the point of intersection of the lines xcos(α)+ysin(α)=a and xsin(α)ycos(α)=b, (α is variable), the point (a,b) lies on the line 3x4y=0 then 9a4+16b4+34 is equal to ...

How high is a parabolic arch of span 24 m and height 18m at a distance of 8 m from the centre of the span? ...

The average cost (Rs. y) of a monthly output of x tons of a irm producing a valuable metal is Rs.((x2/10)3x+62.5).sHOW THAT THE AVERAGE VARIABLE COST CURVE IS A PARABOLA.fIND THE OUTPUT And The cost at the vertex of the para ...

2.the girder of a railway bridge is a parabola with its vertex at the highest point 15m above the ends.if the span is 120 m find the height of the bridge at 24m from the middle point. ...

if x2+y2=a2 then equation of tangent which: 1. passes through (b,0) 2.makes an area of a2 with the coordinate axes ...

Consider the parabola x2 = 4y and circle x2 + (y – 5)2 = r2 (r > 0). Given that the circle touches the parabola at the points P and Q. Let R be the point of intersection of tangents to parabola at P and Q and S be the ce ...

Consider an equilateral triangle ABC with side length 2.1cm. Find the minimum number of equilateral triangles with side length 1cm which can be placed over ΔABC so that it is completely covered. ...

Find the number of integral values of parameter'a'for which three chords of the ellipse x2/2a2 + y2/a2 =1(other than its diameter)passing through the point P(11a, a2/4 )are bisected by the parabola y2=4ax. ...

two fixed pt.s A and B are taken on the axes such that OA=a and OB=b ; two variable point A1 and B1 are taken on the same axes;find the locus of intersection of A1B and B1A: 1. when OA1 + OB1=OA + OB 2. when 1/OA1  1/OB1 = 1 ...

P is the point (1,2) , a variable line through p cuts the axes in A and B . Q is a point on AB such that PA, PQ ,PB are in H.P. find the locus of Q ...

If two opposite vertices of square are (3,4) and (1,1) then the other two vertices are ? ...

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The chord of contact of the pair of tangents drawn from each point on the line 2x+y=4 to the circle {{x}^{2}}+{{y}^{2}}=1 pass through the point a) (1/2, – 1/4) b) (1/2, 1/4) c) (– 1/2, 1/4) d) (– 1/2, – 1/4) ...

If ω be the angle which a focal chord of a parabola makes with the axis, prove that the length of the chord is 4acosec2ω ...

what is the area enclosed within the curve x+y=1 ? ...

1)If α and β are ends of a focal chord of an ellipse of eccentricity e, find tan(α/2).tanβ(/2) 2)Normals drawn to ellipse x2/a2 + y2/b2 =1 at P meet the coordinate axes at A, B. Find the locus of mid point of A and B. 3)A ...