Frequent Co Ordinate Geometry Questions

The coordinates of the point on the parabola y2 = 8x , which is at mininmum distance from circle x2 + (y-6)2 = 1 are (A) (2,-4) (B) (18,12) (C) (2,4) (D) none ...

The coordinates of the extremities of a rod are A(1,2) and B(3,4). S(0,0) is the source of light. The rod AB is parallel to the wall and is midway betwen the point source of light and the wall. CD is the shadow of AB on the w ...

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. ...

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 3x-4y=0 then 9a4+16b4+34 is equal to ...

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. ...

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? ...

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 ...

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

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 ...

given := triangle ABC A→(h,k) a1x +b1y + c1 =0 is the equn of the angle bisector of B(it MAY B INT. AS WEL AS EXTERIOR ) a2x +b2y + c2 =0 is the equn of the angle bisector of C(it MAY B INT. AS WEL AS EXTERIOR ) Find the eq ...

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° ...

The equation of the circle passing through the points (0, 0),(0,b) and (a,b) is a) {{x}^{2}}+{{y}^{2}}+ax+by=0 b) {{x}^{2}}+{{y}^{2}}-ax+by=0 c) {{x}^{2}}+{{y}^{2}}+x+3y=0 d) {{x}^{2}}+{{y}^{2}}+ax-by=0 ...

The equation of the tangent to the parabola {{y}^{2}}=4x+5 parallel to the line y=2x+7 is a) 2x-y-3=0 b) 2x-y+3=0 c) 2x+y+3=0 d) None of these ...

The curve described parametrically by x={{t}^{2}}+t+1,y={{t}^{2}}-t+1 represents a)A pair of straight lines b)An ellipse c)A parabola d)A hyperbola ...

Eccentricity of the parabola {{x}^{2}}-4x-4y+4=0 is__ e=0 __ e=1 __ e>4 __ e=4 ...

The axis of the parabola 9{{y}^{2}}-16x-12y-57=0 is__ 3y=2 __ x+3y=3 __ 2x=3 __ y=3 ...

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