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CBSE
Mathematics
2d coordinate geometry
For the equation \[x + 2y = 8\] find the solution which represents a point on
A) x-axis
B) y-axis

CBSE
Mathematics
2d coordinate geometry
How do you rotate the axes to transform the equation ${x^2} + xy = 3$ into a new equation with no $xy$ term and then find angle of rotation?

CBSE
Mathematics
2d coordinate geometry
Tangents are drawn to a unit circle with centre at the origin from each point on the line \[{\rm{2x + y = 4}}\]. Find the equation to the locus of the middle point of the chord of contact is
CBSE
Mathematics
2d coordinate geometry
The chords of contact of the pair of tangents drawn from each point on the line $2x + y = 4$ to the circle ${x^2} + {y^2} = 1$ passing through the point ______
CBSE
Mathematics
2d coordinate geometry
The centroid of an equilateral triangle is (0, 0). If two vertices of the triangle lie on $x + y = 2\sqrt 2 $, then one of them will have its coordinates
$\left( A \right)\left( {\sqrt 2 + \sqrt 6 ,\sqrt 2 - \sqrt 6 } \right)$
$\left( B \right)\left( {\sqrt 2 + \sqrt 3 ,\sqrt 2 - \sqrt 3 } \right)$
$\left( C \right)\left( {\sqrt 2 + \sqrt 5 ,\sqrt 2 - \sqrt 5 } \right)$
$\left( D \right)\left( {\sqrt 2 ,\sqrt 2 } \right)$

CBSE
Mathematics
2d coordinate geometry
If the eclipse with the equation $9{x^2} + 25{y^2} = 225$ , then find the eccentricity and foci of the eclipse.
CBSE
Mathematics
2d coordinate geometry
Show that the points (-5, 1), (5, 5) and (10, 7) are collinear.
CBSE
Mathematics
2d coordinate geometry
Show that the points A (0, 6), B (2, 1) and C (7, 3) are three corners of a square ABCD.
Find (i) the slope of the diagonal BD and,
(ii) the coordinates of the fourth vertex D.

CBSE
Mathematics
2d coordinate geometry
The line $x=c$ cuts the triangle with corners $\left( 0,0 \right)$, $\left( 1,1 \right)$ and $\left( 9,1 \right)$ into two regions. If the area of the two regions is the same, then find the value of c?

CBSE
Mathematics
2d coordinate geometry
If a pair of linear equations is consistent, then the lines will be
A. Parallel
B. Always coincident
C. Intersecting or coincident
D. Always intersecting

CBSE
Mathematics
2d coordinate geometry
A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a right angle triangle OPQ, where O is the origin. If the area of the triangle is least, then the slope of the line PQ is?

CBSE
Mathematics
2d coordinate geometry
The line L given by \[\dfrac{x}{5} + \dfrac{y}{b} = 1\] passes through the point (13, 32). The line K is parallel to L and has the equation \[\dfrac{x}{c} + \dfrac{y}{3} = 1\]. Then, what is the distance between L and K?
(a). \[\dfrac{{23}}{{\sqrt {15} }}\]
(b). \[\sqrt {17} \]
(c). \[\dfrac{{17}}{{\sqrt {15} }}\]
(d). \[\dfrac{{23}}{{\sqrt {17} }}\]
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