Class 11

Math

Co-ordinate Geometry

Coordinate Geometry

Let $A≡(3,−4),B≡(1,2)˙$ Let $P≡(2k−1,2k+1)$ be a variable point such that $PA+PB$ is the minimum. Then $k$ is 7/9 (b) 0 (c) 7/8 (d) none of these

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Let $0≡(0,0),A≡(0,4),B≡(6,0)˙$ Let $P$ be a moving point such that the area of triangle $POA$ is two times the area of triangle $POB$ . The locus of $P$ will be a straight line whose equation can be

See Fig.3.14. and write the following:(i) The coordinates of B.(ii) The coordinates of C.(iii) The point identified by the coordinates $(3,5)$.(iv) The point identified by the coordinates $(2,4)˙$ (v) The abscissa of the point D. (vi) The ordinate of the points H. (vii) The coordinates of the points L. (viii) The coordinates of the point M.

In each of the following find the value of k for which the points are collinear.(i) $(7,–2),(5,1),(3,k)$ (ii) $(8,1),(k,–4),(2,–5)$

If $x_{1},x_{2},x_{3}$ as well as $y_{1},y_{2},y_{3}$ are in $GP$ with the same common ratio, then the points $(x_{1},y_{1}),(x_{2},y_{2}),$ and $(x_{3},y_{3})˙$ lie on a straight line lie on an ellipse lie on a circle (d) are the vertices of a triangle.

The locus of the moving point whose coordinates are given by $(e_{t}+e_{−t},e_{t}−e_{−t})$ where $t$ is a parameter, is $xy=1$ (b) $x+y=2$ $x_{2}−y_{2}=4$ (d) $x_{2}−y_{2}=2$

Given that $A_{1},A_{2},A_{3},A_{n}$ are $n$ points in a plane whose coordinates are $x_{1},y_{1}),(x_{2},y_{2}),(x_{n},y_{n}),$ respectively. $A_{1}A_{2}$ is bisected at the point $P_{1},P_{1}A_{3}$ is divided in the ratio $A:2$ at $P_{2},P_{2}A_{4}$ is divided in the ratio 1:3 at $P_{3},P_{3}A_{5}$ is divided in the ratio $1:4$ at $P_{4}$ , and so on until all $n$ points are exhausted. Find the final point so obtained.

If the points $(1,1):(0,sec_{2}θ);$ and $(cosec_{2}θ,0)$ are collinear, then find the value of $θ$

Find the ratio in which the line segment joining the points $(–3,10)$ and $(6,–8)$ is divided by $(–1,6).$