class 11

Math

Co-ordinate Geometry

Coordinate Geometry

The centres of those circles which touch the circle, $x_{2}+y_{2}−8x−8y−4=0$, externally and also touch the x-axis, lie on :

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Given the equation $4x_{2}+23 xy+2y_{2}=1$ . Through what angle should the axes be rotated so that the term $xy$ is removed from the transformed equation.

Let $A=(3,4)$ and $B$ is a variable point on the lines $∣x∣$ =6. IF $AB≤4$ , then find the number of position of $B$ with integral coordinates.

See Fig. 3.11 and complete the following statements:(i) The abscissa and the ordinate of the point B are _and _ Hence, the coordinates of B are (__,__).(ii) The x–coordinate and the y–coordinate of the point M are _ and _ respectively. Hence, the coordinates of M are (__,__).(iii) The x–coordinate and the y–coordinate of the point L are _ and _ respectively. Hence, the coordinates of L are (__,__).(iv) The .r–coordinate and the y–coordinate of the point S are _ and _ respectively. Hence, the coordinates of S are (__,__).

Express the polar equation $r=2cosθ$ in rectangular coordinates.

Determine the ratio in which the line 2x +y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3,7).

At what point should the origin be shifted if the coordinates of a point $(4,5)$ become $(−3,9)?$

Find the distance between the points (0, 0) and (36, 15).

The incenter of the triangle with vertices $(1,3 ),(0,0),$ and $(2,0)$ is (a)$(1,23 )$ (b) $(32 ,3 1 )$ (c)$(32 ,23 )$ (d) $(1,3 1 )$