Let me analyze the image to extract the mathematical content and solve the problems for you. PIL import Image import pytesseract

Load the uploaded image

image_path = "/mnt/data/1734959460951dpan2pbg.jpg" image = Image.open(image_path)

Use Tesseract to extract text from the image

extracted_text = pytesseract.image_to_string(image, lang="eng+rus")

extracted_textThe extracted text contains some errors due to the image quality or formatting. However, I will reconstruct the mathematical content based on what is visible and correct it where necessary.

Here's the original content interpreted from the image:

Variant 8:

1. $4x^2 - 21y^2 + 16x + 84y + 268 = 0$, $C(19, -8)$;
2. $x^2 + 4y^2 - 2x - 4y = 2$, $C(1+\sqrt{3}, 0)$;
3. The directrix of a parabola has the equation $y = \frac{13}{8}$, $F(-1, \frac{19}{8})$ is the focus, and $C$ is the point of intersection of the parabola with the $OY$-axis.
4. $2x^2 + 3y^2 - z^2 + 8x - 18y - 2z + 16 = 0$.

Would you like me to solve these problems one by one or clarify any specific part? Let me know!